Like Matt Smith, I do love Patrick Troughton's cosmic hobo, but oh dear oh dear, most of his actual stories are pretty rubbish.
The Second Doctor is at his best in the ensemble pieces The Three Doctors and The Five Doctors, but these are properly Third and Fifth Doctor stories and can't count in this list.
Honourable mentions then are fairly few. There's The Web of Fear,
which featured the unlikely combination of Yetis and the London
Underground and introduced the redoubtable Colonel Lethbridge-Stewart.
Then there's The Invasion
with its scenes of Cybermen marching past London landmarks being
battled by, the now Brigadier, Lethbridge-Stewart and the newly formed
UNIT, who here are all high-tech with an HQ in C-130 Hercules.
And then there's The Tomb of the Cybermen, a blatant rip off of The Mummy's Curse.
When I was young this used to regularly win readers polls as the best
episode ever, mainly voted for by people who'd never seen it as it was
one of the famous Lost Episodes. Then a copy was found down the back of a
filing cabinet and when people actually saw it they found it tedious,
repetitive and pointless. It doesn't win any more.
But amongst all this dross there still has to be a winner, so I'm going to go for The War Games, his last story.
ten episodes its not exactly a story you sit down and watch in one go.
There is also a lot of pointless going over the same ground at a
geological pace and the Doctor is rather less than dynamic too. It
doesn't help that the story gets its own internal geography messed up
too, but there is a lot of atmospheric war-is-hell stuff, which is
actually rather exciting.
However the story really
gets going once the aliens appear. With hindsight the Companions are a
little slow to realise what the boxes that appear with a strange
groaning noise, and which are bigger on the inside than on the outside,
So it may be longer than the Hundred Years War, but it gets there in the end and is a fine way to send off the Second Doctor.