Choose your favourite serial/episode from each of the Doctors eras. Only TV serials/episodes for now. Sorry McGann!
Finally a question for me. I love it when I can make myself feel like I didn't just waste months watching all that stuff. Here I go:
First Doctor: The Time Meddler
The first time they really started mixing historical stories and science fiction stories. Also the first time we see someone else from the Doctors world (the words Gallifrey and Timelords weren't invented yet). Funny, engaging, and one of the better plots of that era. A hint of the glory that was to come in later years.
Runner ups: The very first episode (but not the rest of that story), Marco Polo, The Aztecs, The Gunfighters (very underrated - I love it), The War Machine (very weird and kinda cool to see the first Doctor in a 'present' time story).
Second Doctor: The War Games
They really went all out for Throughton's finale. I love almost his entire run, but this story is unlike any what came before. People often rave about the very end, where he visits Gallifrey for the first time in the show (again without mentioning that name just yet), he gets put on trial and gets executed, and rightfully so, because it's an amazing climax. Everything that came before is just as great though. A proper science fiction classic. Great story, with some very weird (and maybe even Moffat-esque) twists.
Runner ups: Power of the Daleks, The Faceless Ones, Tomb of the Cyberman (my second favorite after War Games), The Abominable Snowmen, Enemy of the World, Seeds of Death.
Third Doctor: The Green Death
I almost went with Three Doctors, which is a lot of fun, but this one edges it out a bit more. Great story, pretty much the perfect climax for the Pertwee era (even though he went on for a while after this). Jo has some great moments in this, and she really is the best Pertwee companion. Sarah Jane is a better companion overall, but she only became really good during Baker's run. Lovely emotional moments towards the end when the Doctor leaves Jo behind, which would later get referenced in Sherlock.
Runner ups: Terror of the Autons, Mind of Evil, The Daemons, The Time Monster (it's crap, but the best kind of crap. Really fun if you're in the right mood), the Three Doctors, and, God help me, Invasion of the Dinosaurs.
Fourth Doctor: City of Death
My very first Doctor Who story ever, after falling in love with Douglas Adams in high school, a couple of years before the new series. Still love it to this day, and I would rank it as my favorite Doctor Who story of them all. I can still sing the theme of this story, even though I haven't seen it in years. Great story that only Adams could write, very funny, and great, great chemistry between the Doctor and Romana. You can really tell that they were in love in real life, and it helps the story tremendously - especially because they actually filmed it in Paris. Everything about this is just great. Watch it! Now!
Runner ups: Ark in Space, Genesis of the Daleks, Brain of Morbius, Seeds of Doom, Deadly Assassin, Talons of Weng-Chiang (apart from the racism), Horror of Fang Rock, Shada (which kind of doesn't count, but it would have been great if it was finished - possibly even better than City of Death. The biggest loss of Who history).
Fifth Doctor: Caves of Androzani
As much as I like Davison, I feel like this era (which actually started towards the end of Tom Baker's run) is where the classic show starts to lose me. Not the fault of the main actors, but it really starts feeling like the show has been running too long at this point. Still, there are some gems among the dirt here and there, and this is one of them. Fun story, good performances, and great location work. Davison is on fire here.
Sixth Doctor: The Two Doctors
Again, I'll be honest, I don't really like any of the stories of Colin Baker's run. Still, this one has Throughton (although they severely misuse him by turning him into a monster for a long part of the story), and the comedy is a bit dodgy, but you can tell Baker is chuffed to work alongside Throughton, the locations are neat, there are a couple of fun jokes and the locations are good. But the best years of the show have passed.
Seventh Doctor: Ghost Light
Ace was good in this. I don't remember a lot about McCoy's stories. The show was getting better, but it just wasn't my thing. I'll see them all again at some point - maybe my opinion will change.
Eight Doctor: Night of the Doctor
The movie was bad.
War Doctor: Day of the Doctor
He was only in this one, except for his cameo at the end of the previous episode. It's a good one though. Really captured the essence of the classic Doctors and represented what was missing in the modern Doctors at that point, while still offering something new.
Ninth Doctor: The Empty Child/The Doctor Dances
Not the biggest fan of the RTD era, but this was a really exciting one at the time. Felt unlike anything else on tv at the time, even though it wasn't that long ago. Or maybe it was. I'm old.
Tenth Doctor: The Girl in the Fireplace
Not a fan of most of Tennant's episodes, but this was a really, really good one. Loved everything about it. Had a very Douglas Adams-like structure. I think I mentioned liking that guy.
Eleventh Doctor: Vincent and the Doctor
If City of Death didn't exist, this would be the best Doctor Who story of all time. Absolutely spectacular. In fact, the entire 5th season of the modern show makes up for the best season of the entire series, but this episode is the topping on that cake. Beautifully layered, perfectly written. I hope we'll get an episode that can match this one day. I mean - an actual Doctor Who story featuring Vincent van Gogh, focusing on his depression, featuring an invisible monster only he can see, which hurts everyone around him and makes everyone think he's crazy, only to find out the monster is just blind, lost and scared. That's mothereffing brilliant, that is. A high point of the entire show, and of the BBC in recent years. They don't make them like this nearly often enough.
Twelfth Doctor: Listen
His season was good, but I still feel like the best is yet to come. I feel like they had to spend some time figuring out how to write for Capaldi's Doctor. This one came closest to cracking that nut, I think. Some great stuff going in this one, and bonus points for making my girlfriend (who is 27) actually hide behind a cushion. Love the ambiguity in whether there actually was a monster or not.
I think it's pretty easy to decipher which flavour of episodes I prefer by looking at these favorites. I never really thought about how much they share, tonally. Huh.