I'm relatively surprised not more posters have shared their lists. I thought at least we'd have all seen NuWho by now, right?
The Tennant era is another favorite of mine, and combined with the Eccleston one, basically the whole of RTD (five years, five series) is my favorite of NuWho, by far. This Doctor simply was extraordinaire. I can't think to say much about him, other than that his era has been rather consistent and, while OTT in many cases, the cast always managed to pay off Davies' wilder concepts (like, well, pulling the planets out of their orbit (!) or Gallifrey appearing next to Earth (!!) or, well, a giant spider nesting in the center of the Earth) and its a testament to that team that these stories are still enduring and entertaining in ways that Moffat stories from later seasons haven't done in repeat viewings.
Many hated RTD for his take on DW, but I didn't. He single-handedly, seemingly, pulled me into this show and, to his credit, forced me to stay. That said... he did kinda ruin Rose, didn't he? She became obsessed with the Tenth Doctor in the second series (OK, maybe she was worried that she'd lose him again or whatever, but still...) and then turned her into... military expert in the parallel world? What?! Honestly, I love the Stolen Earth three-parter, but it'd have been better if she wasn't a fearless, giant-gun-holding soldier. Speaking of which, he positively destroyed Martha in the fourth series by making her a full-fledged soldier, and pairing her with Mickey. Really? What, for the Smith & Jones gag? That lasted long. RTD is also guilty for never bringing the Brigadie into the show (he did in SJA, but it wasn't the same), which is weird given that he grew up with the Third/Fourth Doctors, where the Brigadier was most prominent - I rather he was in The Sontaran Experiment two-parter than Martha, if anything. Still, that is relatively little, as he did so much for the show's legacy - namely, bringing it back, and with a bang - that his shortcomings are just that: short.
As for David Tennant - well, he really is the best Doctor since Tom Baker, isn't he? I mean, 9 is my fave, but strictly objectively speaking, he's the most appealing Doctor that probably ever will be, and the one that showed that NuWho could survive after Eccleston's exit. He helped make the show internationally successful, and thats no small feat. And honestly, I feel he had a couple of years left in him (just like with Eccleston, obviously).
Anyway, the list - I forgot to mention that it'd be nice if we included the animated episodes, cause with them, Tennant has 39 stories (even though I think it really is 38, but whatever).
38. Evolution of the Daleks/Daleks in Manhatten
37. Love & Monsters
36. The Doctor's Daughter
35. The Lazarus Experiment
34. The Next Doctor
33. Fear Her
32. New Earth
31. The Idiot's Lantern
30. Tooth and Claw
29. Planet of the Dead
28. The Christmas Invasion
27. Voyage of the Damned
26. The Infinite Quest (animated)
25. Partners in Crime
24. Rise of the Cybermen/Age of Steel
23. Army of Ghosts/Doomsday
22. Gridlock
21. The Shakespeare Code
20. The Sontaran Stratagem/Poison Sky
19. The Impossible Planet/The Satan Pit
18. Utopia/The Sound of Drums/The Last of the Timelords
17. Dreamland (animated)
16. The Unicorn and the Wasp
15. The End of Time
14. The Runaway Bride
13. Smith and Jones
12. 42
11. Planet of the Ood
10. Turn Left/The Stolen Earth/Journey's End
9 . School Reunion
8 . The Fires of Pompeii
7 . Silence in the Library/Forest of the Dead
6 . Time Crash
5 . The Girl in the Fireplace
4 . Water of Mars
3 . Human Nature/The Family of Blood
2 . Midnight
1 . Blink