The Eight Doctors: Eight and Six manage to uproot all of Time Lord society simply by being clever bastards with a working knowledge of Time Lord law. Then they put their feet up on the Lord President's desk and ask for lunch.
Turlough came cautiously out of the TARDIS. 'So, thanks to that gizmo of yours, that horror has gone back where it came from?'
'Not exactly where it came from,' said the Doctor. 'It's gone back to whoever sent it.'
Turlough nodded thoughtfully.
'Someone's in for a surprise.'
Ryoth's surprise was horrifyingly brief. One moment he was alone in the vault, the next the Drashig was suddenly, terrifyingly there...
The Drashig ate him.
Mad Dogs and Englishmen, which feature a planet of poodle revolutionaries (leading to one of the most hilariously squicky Interspecies Romancesever), Time Lady Shirley Bassey, and Ray Harryhausen declaring war on George Lucas and invading his home with stop-motion figurines. Then there's this memorable exchange:
Poodle: You said this was a time ship?
Doctor: You know of such things?
Poodle: We are poodles, Doctor! Of course we know of such things!
Unnatural History has a rift in space-time making San Francisco even weirder, the Doctor being called "a backrub slut", Fitz being mugged by a unicorn in the middle of an alleyway for a bar of chocolate, and other gems.
After the Doctor meets up with Fitz again:
‘What’s the surrealism report?’
Fitz spread out his map of the city, turned the pages of his notebook. ‘The plants in Golden Gate Park are growing at five times the normal rate – it’s closed to the public. Lots of unconfirmed cryptozoological sightings, including an alleged vehicle theft by Bigfoot. Oh, and would you believe Lombard Street has gone straight?’
‘Well,’ laughed the Doctor, ‘as long as Castro Street hasn’t gone straight. . . ’
When Fitz explains why he's quitting smoking:
‘It’s the Law of Conservation of Niceness,’ he said. ‘It’s a fundamental principle of the universe, like Schrodinger’s cat or Heisenberg’s knickers.’ He twirled the chocolate bar in his fingers. ‘The Doctor’s always got to have someone around who can be fluffy and sympathetic. With your alter ego gone, for the safety of the cosmos, I have to make the supreme sacrifice. Give up smoking. And practise saying “Gosh wow!”’
Another when talking to Sam about drugs:
‘The last time I dropped acid was back in 1968,' [the Doctor] said.
She nearly dropped her cigarette with surprise. He said, ‘I needed an altered state of consciousness to contact a discarnate entity. But I was almost transformed into a psychopathic Aztec god.’
She stared. ‘Now that is a bad trip.’
In Seeing I the Doctor needs information, so he uploads 6.02 x 10^23 data-umphs to the corporate network. The programs appear to have something of their creator's Cloud Cuckoo Lander personality...
As they ran about they budded off subprocesses hither and yon. As they budded they mutated, with new subroutines turning up from nowhere. Imogen found itself afflicted with a particularly odd strain of umph which spray painted KILROY WOZ ’ERE graphics all over its annual report. Kisumu Interplanetary’s intranet collapsed as several thousand umphs engaged its computer power in playing eight-dimensional Tetris.
Later he needs the INC people distracted so he can use one of their computers: he logs on, fires hundreds of employees, hires hundreds more, creates working parties and working parties to monitor them and orders sandwiches for everybody. Wonderful chaos ensues.