Yeah, I'd like a more human doctor. I'd like him to be darker than previous incarnations, maybe a bit depressing even.
I don't think we are going to see a darker Doctor because so much of his emotional baggage is gone with the revelation the Timelords were not wiped out by him and the fact that they are out there waiting to return. Also a new lease of life with 13 new regenerations so he doesn't have to worry about death. I feel we will see a very Tom Baker silly role esq Doctor.
I don't need darker. Smith had plenty of dark times throughout his run. I would, however, like a less manic Doctor. Tennant had a lot of screaming and running. Smith had a lot of flailing about and talking-way-too-fast-sometimes. Maybe this time we could go for someone more subdued. Not darker...just quieter.
I'm quite all right with not having "something dark." Doctor Who is a family show about an alien with a time machine whose idea of fun is having adventures in time and space. If I want something dark, I'll break out my Battlestar Galactica or Breaking Bad Blu-rays.
I think the Twelfth Doctor will be a tough old bastard that will put the fear of God into anyone who gets on his bad side (Daleks, Cybermen, etc). He'll also be very funny and charming at times, echoing some of the earliest Doctors in that regard.
Before the Specials, I would've liked to see him secretive and Plotting (cleaning up past mistakes/oversights) like McCoy's later run, but, I think we've turned away from that plot direction with all the developments in the Specials. I expect him to be somewhere between Davison and T. Baker. Charming and polite like Davison, but, not as dark, as Davison got, mixed with a bit of the jovial prankster Tom Baker portrayed.
We haven't had very many serious, straightforward doctors, and none since the ninth. I'd like to see a doctor more like the third or fifth, less manic, alien, or silly.
I see him as somewhat manic and abrupt with everyone aside from his companions and any other close friends he might have. Colin Baker like but without the horrible technicolour dreamcoat and tendency to strangle.
I don't want darker or depressing, but I would like a much less over the top eccentric Doctor. Perhaps one closer to ninel minus the angst or maybe like Hurts Doctor. They seem to have looked at "eccentric" in the character profile and replaced it with "manic nutcase who could open a quirky quirk shop". Even season 16 didn't have the 4th Doctor acting that over the top.
I think one thing that will change is less mooning over his young female companions (reintroduction of a male companion to allow for the aromatic component?) because of the age differential between actors.
Oh I hate male companions! Male companions are rarely ever good. And how on Earth is Matt Smith dark? He's probably the lightest doctor we've had in a long time. I want some akin to Eccleston and Hurt with this doctor and with some of the sarcasm that Davison and even a bit of C. Baker had. I don't really want much Tom Baker in him though, I'm not a big fan of his and we had a fair share of that in Tennant anyway. Oh, maybe a bit of the mysterious later seventh doctorness that someone mentioned on here would be good. But yeah, definitely sarcastic.
I didn't say he needed a male companion. He could be gay and still travel with a girl. You could make him gay and give Captain Jack a reason to come back! Wouldn't that just make his day? And the Colonel Runaway scene from "A Good Man Goes to War" is all the evidence you need that Matt Smith's Doctor has a dark side.
I wasn't replying to you, I was just talking in general. :P Well if we had a gay doctor, I'd like an over the top camp doctor which would exclaim words like "ew", "yucky" and his catchphrase could be "you so have no taste!" :P