Moira from Fallout3. She's too happy and cheery, annoys the hell out of me. That and, oh yeah, her quests nearly kill you!
Rochelle, L4D2 - she just isn't Zoey.
Tali, Kaiden, Ashley and Jack from ME/ME2. All whiney and annoying.
But the character I hate the most, with unbrideled passion?
Edge, Ace Combat 5.
Get off your fucking high-horse you moaning *****! You're a fucking fighter pilot, you're going to end up killing people, get over yourself! And that voice...goes through me like fingernails on a chalk board. Honestly the most annoying character I have ever come across in a game. When Chopper went down, I was in tears. Of rage that is. Why couldn't Edge have bought it instead?
(That said, Ace Combat seems to have a thing for annoying characters, the wife in AC6 sent me round the bend too...)