System Shock 2 stuck with me alot:
"Look at you, Hacker. A pathetic creature of meat and bone, panting and sweating as you run through my corridors." - SHODAN
"Silence the Discord" - The Many Hybrid.
"I believe the plans the Many have for me are greater than I even imagined. The change is upon me. But the path is more glorious than we imagined. It does not stop at a mere single mutation... the form I've been promised is more beautiful than even that... They tell me I will float through the air and strike at the foes of our biomass with my mind... with our mind... my cup runneth over..." William Bedford Diego
A lot of the reason they stuck with me was because of the excellent work of the audio engineers. They really made the mood of SS2. Go listen [http://www.systemshock.org/shocklogs/] to some of the audio logs (in particular the one I reference above. It's about half-way down the page) and you'll hear how creepy they managed to make it.
"Good morning, and welcome to the Black Mesa Transit System..."
"They're waiting for you Gordon. In the test chamber."
"Ewww, what's that stench?!?"
-Half-Life
As for more modern games, mostly I'd have to say stuff from World of Warcraft, like Bal'a dash, malanore, and Lok'Tar... OH, and the big ones:
"Akama... I find your duplicity hardly surprising... I should've exterminated you and your malformed bretheren long ago..." Illidan Stormrage
"So... the Light's vaunted justice has finally arrived..." Arthas, The Lich King
You would think that Blizzard would be smart enough to put some sort of mechanism for skipping over long speeches that take place before starting a boss-battle, but no... and as a result, I have heard both those speeches about a Hojillion times. If you'll excuse me now, I must go lobotomize myself with a dull icepick.