Here is a list of quotes from various talks etc.

Michael Atiyah
(at the start of his talk) "Thank you. You're supposed to wait until the end to applaud."

Raphael Clifford
"What's wrong with promiscuity? A question you may well have asked yourself."
"The moral of the story, for anyone who likes morals ..."

Erik Demaine
"An infinite family of sculptures. We've only built finitely many so far."
"So the natural thing to do is to build a physical model of the theoretical model of the physical piece of paper"
"It's impossible to fold a piece of paper like this" (holding up a folded piece of paper)
"It's good to work with things that exist"
"This is a game called Rengo Kriegspiel. It is Go, blindfold, ... in teams"

Tim Gowers
(on why he uses the notation \mathbf{Z}_N) "Lots of people HATE the notation \mathbf{Z}_N, ... but I don't."
"I've left 10 minutes to tell you about ergodic theory ... let's very quickly say what a dynamic system is."
"You take a huge baker's equivalent of a butcher's cleaver."
"Let me give you a wrong proof ... since it's wrong, I better not write it down."
"If you add the magic word 'Tao'"
"It's a bit like taking the circle, except it's an infinite circle."
"I can say a lot about hypergraph regularity just by telling you about graph regularity ... but can I do it in 1 minute?" (1 minute from the end of his talk)
"Something called Szemerédi's Regularity Lemma, which I'm really not going to try to do in 3 minutes"

Markus Jalsenius
"I'm having the same problem as everyone else, namely time constraints, so I'll have to rush through [screensaver turns on]"

Gil Kalai
"Dictatorship has some ... disadvantages"

Stephan Kreutzer
"This graph is tree-like: If you're sitting at the back an have sufficiently bad eyesight then it looks like a tree"

Antony McCabe
"I'm not quite sure what the postage is on two paper clips, but it's a restriction."

Richard Mycroft
"We use the regularity lemma, so when I say large, I mean large"
"So finally, my 2 minute explanation of a 40 page paper"

Alexandru Popa
"Again, I will use my hand as a stick."

Samir Siksek
"100,000 dollars is not really a lot of money, which is my excuse for not trying to solve it."

Matas Sileikis
"I do not write the trivial calculations"

Unattributed
"Our only candidate today is Shiva ... erm, Shiva." (introducing the speaker Shiva Kasiviswanathan)