I thought I'd list what my top three stories from each doctor are. You guys'll probably join in. 
First Doctor:
Hmm, I'm struggling with the First Doctor a bit as I've not seen that much with him in.
1) The Celestial Toymaker - Only seen the surviving episode (duh) but I loved it, I know if I saw the whole thing it'd be my top Hartnel story and one of my favourites in general
2) An Unearthly Child - Just the first episode.
3) The Daleks - Beats Invasion of Earth IMO, but I've not seen either for years so my opinion may have shifted.
Second Doctor:
From what I've heard, if I saw Enemy of the World it might be high up, but as it is I've not seen it.
1) Tomb of the Cybermen - An excellent story, love the 60s sci-fi feel. Certainly the best story from the 1960s that I've seen.
2) The Moonbase - Only seen the surviving episodes. But I really liked it, maybe more so than Tomb, but as I've only seen pretty much half of the story then I can't rate it as number one. Maybe if I saw the serial with the animated episodes added then it may take the top spot.
3) The Seeds of Death - Not seen it in a while but I prefer it to the other whole Troughton serials I've seen (which haven't been added already). Can I confess right here that I've not seen many of his whole serials for some reason, they never seemed to stock that many at an affordable price. But I've seen quite a lot of surviving episodes from lost serials.
Third Doctor:
1) The Three Doctors - This and my second favourite are pretty close but this came out on top as I just love it and after seeing it many times, I still don't tire of it. Way superior to The Five Doctor and on the same level as Day of the Doctors (thought I can't say which I prefer as I love them for so very different reasons). Just a perfect Doctor Who story.
2) Planet of the Spiders - Don't judge me! I love this story. Would have been better if it was an episode or two shorter but for the first four episodes I was absolutely loving it! And this is a rare instance when I got goose bumps watching a classic serial. The scene where the queen spider sort of controls the doctor and senses his fear was superb! Possibly my second or third favourite regeneration story, but I've not ordered them in a while. But this is near the top either way.
3) The Green Death - The green maggots are awesome! I remember in primary school I drew some green maggots and cut them out. People had no clue what they were as I was probably the only kid who watched classic who.
Fourth Doctor:
Before I get a bollocking, I'm gonna confess I'm not a very big fourth doctor fan. I like the actual doctor but I wasn't so fussed about the stories much. But I've not watched them for years, so maybe I need to have a big re-watch and re-decide my opinions.
1) The Keeper of Traken - I didn't like this much as a kid but I've now grown to really love this serial, now more so than Logopolis (if you told an 11 year old me I'd be saying this now, I'd have laughed in your face). Such great story telling and style. It's a shame there weren't more 80s stories like this.
2) Logopolis - What can I say, nostalgia! As a kid this was pretty much the story I'd always go to when I was in the mood, this is probably my most watched Doctor Who ever. That may be the reason it's not my favourite anymore though, because I've seen it so many times. Oh well, still awesome!
3) The Horror of Fang Rock - As I've said I'm not a huge Fourth Doctor fan and this isn't really one of my favourite stories ever but compared with other fourth doctor tales, this wins. Note though that I've not seen them in a while so opinions may change. But for now it is how it is.
Fifth Doctor:
1) The Caves of Androzani - I hate to agree with most other fans but this story is simply outstanding. Best regeneration ever. The emotion, the style, the story, the acting, the everything!
2) Earthshock - The first classic story I ever saw. I'm glad my dad picked this one out for me as if I had chosen myself, chances are I'd have chosen a long and drawn about Tom Baker serial and I may not be the big whovian I am now. A fun fun story, when I first got it I watched it back to back over and over again. Still holds up today.
3) The Five Doctors - I don't love this story, but I prefer it to the rest of the Davison era. Yet again note I've not seen that many Davison stories (quite a few though) but the others I've seen haven't been spectacular. But yeah it's still a good story though.
Sixth Doctor:
Here I'm spoilt for choice, as I just love the Colin Baker era. I know what you must think of me right now. Note all of them are very close together.
1) The Two Doctors - My traditional favourite, I've loved this story for a long time. It has a unique style from other stories plus the back and forth between Troughton and Baker are outstanding. I love everything in this. This is the perfect Doctor Who story, there's nothing wrong with it!
2) Revelation of the Daleks - Just an awesome story, probably the darkest Doctor Who ever IMO. It's probably the story that served inspiration for the Eccleston Dalek stories, and we all know how good that is. I was surprised by how mature and adult this story is, I thought some of the stuff they're getting away with here they couldn't get away with even today! I just adore this story!
3) Vengeance on Varos - I can't believe this is so low on the list, this could top most of what I've put as number one on most other Doctors. To me this is pretty much as good as Androzani, I see a lot of similarities in it. The style, the story, the everything. I absolutely love this! Sil is awesome, everything is awesome! Once again a more mature story then I remembered when I was a kid. Modern Doctor Who could take a nod or two from this.
Seventh Doctor:
Bit more of a struggle here as lets face it, there's not been that many great Seventh Doctor stories, but the great ones are usually very great. Note there's also quite a few popular stories I've not seen yet.
1) Remembrance of the Daleks - I preferred my number two story as a kid, but now I like this. Also quite mature and is a great story.
2) Survival - Probably the second most watched Doctor Who story for me, it's up there with Logopolis. But yet again because I've seen it so many times it suffers from that. Still, a great story and I could think of worse ways to end the classic series.
3) Ghost Light - Not a favourite as a child, in fact I used to find it rather boring. But when I recently re-watched this I was pleasantly surprised. I've not seen Curse of Fenric yet (which has been sitting in my DVD rack since Christmas unwatched) so I'm not sure whether that could over-take anything but in my current situation, Ghost Light is a pretty cool story.
Eighth Doctor:
Obviously I can't do a top three for the Eighth Doctor as he's appeared in two stories. But out of his two I'd rate the movie above Night of the Doctor because it's one of my most watched Doctor Who's' ever (it's up there with Logopolis, The Two Doctors and Survival) and I still love it today. Mind you I still love Night of the Doctor.
Ninth Doctor:
Yet again, all of these are pretty close. There's not such thing as a Ninth Doctor story I dislike. In fact I love most if not all of them.
1) Dalek - Just superb. Nuff said.
2) Bad Wolf/The Parting of Ways - Also superb. You can't beat Ninth Doctor with Daleks. Not easily anyway.
3) Aliens in London/World War Three - Another terrific story. The Slitheen were my first favourite monsters and were for years until one day the Master took first place. Another great story and anyone who goes on about "stupid green aliens that keep farting" will get a knuckle sandwich from me.
Tenth Doctor:
This is probably the hardest for me to do actually. There's been so much goodness from this era. Okay, let me try but I may re-arrange this at a later date.
1) Rise of the Cybermen/The Age of Steel - This is an excellent story, I absolutely love it. Utterly entertaining. I miss these Cyberman.
2) The End of Time - Nostalgia, it's all nostalgia! I know it's not that great but I'm very nostalgic over this story and I can't really think of anything else right now.
3) The Sound of Drums/Last of the Timelords - More nostalgia! While I do acknowledge this is better than the End of Time, I need to do some more re-watching and I'm not as nostalgic about this. But yeah, this is utterly awesome.
Eleventh Doctor:
Wow, there's been so much shit in this era it's really easy to choose the top episodes, as there's not that many to choose from.
1) The Day of the Doctor - The only Matt Smith episode on par with the Tennant era. This is just superb!
2) The Angels Take Manhattan - A fantastic story and gets rid of the companions I hate the most! Great story telling, most of this is awesome. Easily the best of series 7.
3) Cold War - I struggled choosing third place. Originally I'd have chosen The Impossible Astronaut/Day of the Moon but on a re-watch I found it utterly boring (I loved it before though). And I've loved this since day one. Just awesome! Note Eleventh Hour would also be high up.
Twelfth Doctor:
I know he's done five episodes so far but I can just change this if I see another one I prefer.
1) Deep Breath - A really cool episode.
2) Robot of Sherwood - Surprised by how much I like this episode, I seem to like it more than most other people. I don't usually go for humour in Doctor Who but there's something different about this episode for me. it was entreating and didn't use quite as feeble humour as the Smith era.
3) Into the Dalek - What can I say, I like this.
First Doctor:
Hmm, I'm struggling with the First Doctor a bit as I've not seen that much with him in.
1) The Celestial Toymaker - Only seen the surviving episode (duh) but I loved it, I know if I saw the whole thing it'd be my top Hartnel story and one of my favourites in general
2) An Unearthly Child - Just the first episode.
3) The Daleks - Beats Invasion of Earth IMO, but I've not seen either for years so my opinion may have shifted.
Second Doctor:
From what I've heard, if I saw Enemy of the World it might be high up, but as it is I've not seen it.
1) Tomb of the Cybermen - An excellent story, love the 60s sci-fi feel. Certainly the best story from the 1960s that I've seen.
2) The Moonbase - Only seen the surviving episodes. But I really liked it, maybe more so than Tomb, but as I've only seen pretty much half of the story then I can't rate it as number one. Maybe if I saw the serial with the animated episodes added then it may take the top spot.
3) The Seeds of Death - Not seen it in a while but I prefer it to the other whole Troughton serials I've seen (which haven't been added already). Can I confess right here that I've not seen many of his whole serials for some reason, they never seemed to stock that many at an affordable price. But I've seen quite a lot of surviving episodes from lost serials.
Third Doctor:
1) The Three Doctors - This and my second favourite are pretty close but this came out on top as I just love it and after seeing it many times, I still don't tire of it. Way superior to The Five Doctor and on the same level as Day of the Doctors (thought I can't say which I prefer as I love them for so very different reasons). Just a perfect Doctor Who story.
2) Planet of the Spiders - Don't judge me! I love this story. Would have been better if it was an episode or two shorter but for the first four episodes I was absolutely loving it! And this is a rare instance when I got goose bumps watching a classic serial. The scene where the queen spider sort of controls the doctor and senses his fear was superb! Possibly my second or third favourite regeneration story, but I've not ordered them in a while. But this is near the top either way.
3) The Green Death - The green maggots are awesome! I remember in primary school I drew some green maggots and cut them out. People had no clue what they were as I was probably the only kid who watched classic who.
Fourth Doctor:
Before I get a bollocking, I'm gonna confess I'm not a very big fourth doctor fan. I like the actual doctor but I wasn't so fussed about the stories much. But I've not watched them for years, so maybe I need to have a big re-watch and re-decide my opinions.
1) The Keeper of Traken - I didn't like this much as a kid but I've now grown to really love this serial, now more so than Logopolis (if you told an 11 year old me I'd be saying this now, I'd have laughed in your face). Such great story telling and style. It's a shame there weren't more 80s stories like this.
2) Logopolis - What can I say, nostalgia! As a kid this was pretty much the story I'd always go to when I was in the mood, this is probably my most watched Doctor Who ever. That may be the reason it's not my favourite anymore though, because I've seen it so many times. Oh well, still awesome!
3) The Horror of Fang Rock - As I've said I'm not a huge Fourth Doctor fan and this isn't really one of my favourite stories ever but compared with other fourth doctor tales, this wins. Note though that I've not seen them in a while so opinions may change. But for now it is how it is.
Fifth Doctor:
1) The Caves of Androzani - I hate to agree with most other fans but this story is simply outstanding. Best regeneration ever. The emotion, the style, the story, the acting, the everything!
2) Earthshock - The first classic story I ever saw. I'm glad my dad picked this one out for me as if I had chosen myself, chances are I'd have chosen a long and drawn about Tom Baker serial and I may not be the big whovian I am now. A fun fun story, when I first got it I watched it back to back over and over again. Still holds up today.
3) The Five Doctors - I don't love this story, but I prefer it to the rest of the Davison era. Yet again note I've not seen that many Davison stories (quite a few though) but the others I've seen haven't been spectacular. But yeah it's still a good story though.
Sixth Doctor:
Here I'm spoilt for choice, as I just love the Colin Baker era. I know what you must think of me right now.
Note all of them are very close together.1) The Two Doctors - My traditional favourite, I've loved this story for a long time. It has a unique style from other stories plus the back and forth between Troughton and Baker are outstanding. I love everything in this. This is the perfect Doctor Who story, there's nothing wrong with it!
2) Revelation of the Daleks - Just an awesome story, probably the darkest Doctor Who ever IMO. It's probably the story that served inspiration for the Eccleston Dalek stories, and we all know how good that is. I was surprised by how mature and adult this story is, I thought some of the stuff they're getting away with here they couldn't get away with even today! I just adore this story!
3) Vengeance on Varos - I can't believe this is so low on the list, this could top most of what I've put as number one on most other Doctors. To me this is pretty much as good as Androzani, I see a lot of similarities in it. The style, the story, the everything. I absolutely love this! Sil is awesome, everything is awesome! Once again a more mature story then I remembered when I was a kid. Modern Doctor Who could take a nod or two from this.
Seventh Doctor:
Bit more of a struggle here as lets face it, there's not been that many great Seventh Doctor stories, but the great ones are usually very great. Note there's also quite a few popular stories I've not seen yet.
1) Remembrance of the Daleks - I preferred my number two story as a kid, but now I like this. Also quite mature and is a great story.
2) Survival - Probably the second most watched Doctor Who story for me, it's up there with Logopolis. But yet again because I've seen it so many times it suffers from that. Still, a great story and I could think of worse ways to end the classic series.
3) Ghost Light - Not a favourite as a child, in fact I used to find it rather boring. But when I recently re-watched this I was pleasantly surprised. I've not seen Curse of Fenric yet (which has been sitting in my DVD rack since Christmas unwatched) so I'm not sure whether that could over-take anything but in my current situation, Ghost Light is a pretty cool story.
Eighth Doctor:
Obviously I can't do a top three for the Eighth Doctor as he's appeared in two stories. But out of his two I'd rate the movie above Night of the Doctor because it's one of my most watched Doctor Who's' ever (it's up there with Logopolis, The Two Doctors and Survival) and I still love it today. Mind you I still love Night of the Doctor.
Ninth Doctor:
Yet again, all of these are pretty close. There's not such thing as a Ninth Doctor story I dislike. In fact I love most if not all of them.
1) Dalek - Just superb. Nuff said.
2) Bad Wolf/The Parting of Ways - Also superb. You can't beat Ninth Doctor with Daleks. Not easily anyway.
3) Aliens in London/World War Three - Another terrific story. The Slitheen were my first favourite monsters and were for years until one day the Master took first place. Another great story and anyone who goes on about "stupid green aliens that keep farting" will get a knuckle sandwich from me.
Tenth Doctor:
This is probably the hardest for me to do actually. There's been so much goodness from this era. Okay, let me try but I may re-arrange this at a later date.
1) Rise of the Cybermen/The Age of Steel - This is an excellent story, I absolutely love it. Utterly entertaining. I miss these Cyberman.
2) The End of Time - Nostalgia, it's all nostalgia! I know it's not that great but I'm very nostalgic over this story and I can't really think of anything else right now.
3) The Sound of Drums/Last of the Timelords - More nostalgia! While I do acknowledge this is better than the End of Time, I need to do some more re-watching and I'm not as nostalgic about this. But yeah, this is utterly awesome.
Eleventh Doctor:
Wow, there's been so much shit in this era it's really easy to choose the top episodes, as there's not that many to choose from.
1) The Day of the Doctor - The only Matt Smith episode on par with the Tennant era. This is just superb!
2) The Angels Take Manhattan - A fantastic story and gets rid of the companions I hate the most! Great story telling, most of this is awesome. Easily the best of series 7.
3) Cold War - I struggled choosing third place. Originally I'd have chosen The Impossible Astronaut/Day of the Moon but on a re-watch I found it utterly boring (I loved it before though). And I've loved this since day one. Just awesome! Note Eleventh Hour would also be high up.
Twelfth Doctor:
I know he's done five episodes so far but I can just change this if I see another one I prefer.
1) Deep Breath - A really cool episode.
2) Robot of Sherwood - Surprised by how much I like this episode, I seem to like it more than most other people. I don't usually go for humour in Doctor Who but there's something different about this episode for me. it was entreating and didn't use quite as feeble humour as the Smith era.
3) Into the Dalek - What can I say, I like this.
