Disclaimer: I count the Big Finish audioplays as episodes, as per BBC Policy that canon-is-what-you-make-it.
1) The Tenth Planet
I've read the script of the episode, and seen the surviving scenes accompanied by full audio. The Cybermen are the most horrifying villain in the early series, their sing-song voices, patchwork self-mutilation and cold ruthlessness make them a fitting enemy for The Doctor's final outing. The mystery of the regeneration give the episode a magical, ethereal touch.
(Runner Up : The Dalek Invasion of Earth - Well paced, action-packed, and a brilliant surprising ending)
2) The Power of the Daleks
Reading the script and listening to the audio, I think this is the best Dalek story ever told. Troughton's first appearance sees him trying to regain the trust of his companions, while fighting the manipulative machinations of three unarmed Daleks. The Daleks themselves have never been so efficient, cunning and ruthless, playing the humans against each other, stealing resources and covertly building an army. Troughton is fantastic, the story is interesting, and the Daleks are blood-hungry bastards.
(Runner Up: The War Games - Yes, its overly long, but the last three episodes are masterful. Troughton's speech to the Time Lords, justifying his existence is some of the best acting in the entire 40+ years).
3) Death to the Daleks
I really like this episode. The Doctor and the Daleks, trapped on a mysterious world where their advanced technology is inoperable, are forced to rely on each other to survive. The developing mystery of the planet's inhabitants, and the navigation of the ancient temple that dampens electricity, is a fun adventure.
(Runner Up: Terror of the Autons - The Master at his best, some brilliant interplay between Pertwee and Delgado and a great story)
4) Genesis of the Daleks.
Another Dalek choice, and a cliche at that, but I don't care. This is one of my favourite Doctor Who productions. It still holds up well, the Thals and Kaleds eternal war is realised well through allusion, dialogue and attitude. Most of the characters are interesting (Davros is fucking marvellous), and the writing produces some really powerful scenes.
WE OBEY NO ONE. WE WILL PREPARE. WE WILL GROW STRONGER. WHEN THE TIME IS RIGHT, WE WILL EMERGE, AND TAKE OUR OUR RIGHTFUL PLACE, AS THE SUPREME POWER OF THE UNIVERSE.
(Runner Up: Pyramids of Mars. A great story with an incredible villain. There's a great tension in this show, as The Doctor meets his Devil. Flawless.)
5) Spare Parts
The prequel to "The Tenth Planet", and the genesis of the Cybermen. This is one of the greatest Doctor Who story ever, being incredibly intellgent, supremely acted, and chilling to the bone. The story of Mondas, and its witty, religious, flawed, charming, hopeful and desperate people is the most tragic tale of the Whoniverse. Everyone brings their A-game to this.
(Runner Up: Omega - The best plot twist in the series, had me fucking floored. Redeems the tragic Omege an brilliant, brilliant ways)
6) Arrangements for War
My favourite Doctor and my favourite companion, on a world in the middle of a simple war. A beautiful story, in which The Doctor fights war and peace to unite two lovers, with an ending that left me catatonic with shock. The Doctor's rage at the end, his fury against fate, is the most emotional moment in the series.
(Runners Up: Too many to choose from! The Holy Terror starts off as darkly witty and finishes as darkly horrific; Jubilee is a brilliant contrast, the mania of an overpowered and deranged British Empire, juxtaposed with a lone Dalek's gradual quiet understanding of sentience (and thus madness); The One Doctor - a genuine, laugh-out-loud comedy.
Okay, if I have to pick one: Davros - the story of two "men of destiny". Davros and The Doctor working together, with the former genuinely exploring redemption, and the latter shooting it down. The flashbacks to Skaro and the hellish war that bore the evil, suffering genius, are a brilliant contrast to the priveledged, fortunate Time Lord.)
7) LIVE-34
An experimental story, in which a planet's repression by a brutal dictator, its rebellion and defiance, are told through a series of scenes from a radio news/talk show. The Doctor's appearances, in the media interviews, undercover investigations, news broadcasts, are incredibly effective and real. You get a real insight into how much of a cunning bastard The Doctor can be in this story.
(Runner Up - Master - The Doctor makes a deal with the Devil, and the Master is stripped of his identity. An amazing character piece, in which the Seventh Doctor tries to redeem his oldest friend)
8) The Natural History of Fear
The darkest, most pyschologically haunting episode of Doctor Who. Its very difficult to describe, but we hear familar voices playing out different roles and characters in a repressive city that tells its inhabitants what to think, feel, say and love. Throughout these many characters, The Doctor and his Companions begin to slowly assert pieces of their broken selves. Don't expect to understand it fully first time round.
(Runner up - Storm Warning - Our reintroduction to the Eight Doctor after the TV movie, and a fun action-adventure. Worth listening to as it massively pisses all over the movie, of which it comes straight after).
9) The Empty Child / The Doctor Dances
Creepy, clever, fun, fan-fucking-tastic! Every moment is interesting, every scene is gold.
(Runner up - Dalek - The vengeful Doctor and his lonely enemy. We get some great Dalek-action and scenes that define the hurt post-war Doctor)
10. Girl in the Fireplace
One of the most imaginative ideas ever, perfectly realised. This episode is flawless.
(Runner up - either Human Nature/Family of Blood or Silence in the Library/Forest of the Dead. Both are fucking amazing.)