Anyway, my favorite episode...hmm. I can't decide, so I'll do it by season (series, but I'll call them season to avoid getting confusing). Note that I've only watched the new seasons. Here be spoilers.
Season 1: Dalek. It was the first time I ever saw a Dalek, and it was so creepy. The fact that one weakened Dalek was capable of taking down that huge base was utterly terrifying. Not that I don't like having loads of Daleks around, but it ramps down the creep factor a bit. And of course the Dalek's suicide at the end
Season 2: The Impossible Planet/The Satan Pit. This wasn't my favorite season, but it was good enough. I liked the themes of the episode, and the Ood were fabulous. And of course, finding an ancient god was a novel enough idea for Doctor Who that it was quite exciting. The part where they were trapped and getting chased was good too, although a bit cheesy. I almost chose The Girl in the Fireplace but it was reeeaaallly sexist and wasn't too good to Rose or Mickey. It didn't have too much continuity with the previous episode, either.
Season 3: This would have to be a tie between Blink and Utopia/The Sound of Drums/Last of the Time Lords. Blink was well-paced, simple, and creepy. It was less sexist than most of Moffat's episodes, but it still had some issues: it romanticized stalking and it had Sally falling in love with Larry as a sign of her getting over the angels. Those two things got me down a bit. As for the finale episodes, I really enjoyed the relationship between the Doctor and the Master, and the Master himself was freewheeling and way over the top. I was happy to see Captain Jack back, and Martha's character development, along with her family's, was quite good. And the scene where the Doctor begs the Master to regenerate still makes me tear up.
Season 4: There are so many good episodes in this season that I don't know where to start. Planet of the Ood was emotional and clever. Partners in Crime was extremely funny—remember Donna and the Doctor having their wordless conversation through the window? Silence in the Library/Forest of the Dead progressed at an excellent pace most of the time (although there was a weird bit toward the middle of the first episode) and the mystery was engaging. It also introduced River Song, in what I quite possibly might consider her best episode, as it was prior to her flanderization as a StrongWomanTM and disturbing obsession with the Doctor that's portrayed as positive (as well as a bunch of other problems). And Moffat, for all his faults, is quite creative when it comes to coming up with villains (although he seems to have gotten lazier and more arrogant after he become showrunner). The Vashta Nerada were intriguing and scary, and less gimmicky than some of Moffat's other monsters (although that may be because they only appeared in one episode). The only major problem I had with it was that Moffat repeated his habit of putting the companion into an unimportant role and making the episode primarily Doctor-centric.
Season 4 Specials: I have to go with The End of Time, due to the Doctor's wonderful interactions with Wilf (I LOVE WILF) as well as the Doctor finally getting pushed past his breaking point. This is actually one of my issues with Moffat's writing: he tries to do this too often, and it feels forced and unexciting as a result. The Waters of Mars comes in a close second: almost disturbingly creepy, due to both the water virus and the Time Lord Victorious, it also brings in a huge load of character development for the Doctor.
Season 5: The Pandorica Opens/The Big Bang. What can I say? I like flashy, and Moffat's plots were still making a reasonable amount of sense at this time. Vincent and the Doctor was also quite good, not to mention that it had Nu Who's best portrayal of mental illness to date, but I wasn't as impressed by it as some people seem to be.
Season 6: The Impossible Astronaut/Day of the Moon. I still like River in this episode (it isn't until later this season that her character gets really bad), and I also like flashy. And plot advancement. It did feature the Doctor abandoning his principles and committing genocide for little reason, though, which was a big letdown in terms of his character but not something that was limited exclusively to this episode. I also liked The Doctor's Wife andThe God Complex.
Season 7, Part 1: The Angels Take Manhattan. This is mostly by elimination of everything else; although I was quite impressed the first time I saw it, the whole thing falls apart when you examine the details.
Season 7, Part 2 (including the 2013 specials): The Crimson Horror. It was plagued with issues just like the rest of season 7 (sexual assault and a stupid joke where the Doctor thinks a married lesbian woman is sexy because she's wearing tight clothes), but at least it didn't have much of Clara in it, and the plot was reasonably interesting.
So there you have it: my favorite episodes of Doctor Who.
~dlgn