Well I certainly get annoyed when games start making prominent female characters into ey candy for the juvenile masses, but that's a fairly common complaint so I don't think I need to go into too much detail.
I also hate it when games put you into 'forced vehicle sections' like in say Gears of War 2, because while the actual cover/combat aspect of the game is perfect, the car never controls as well and just generally isn't much fun to use. Plus, the fact that I can't leave the car means I often feel trapped, like I'm wasting time waiting for the actual game to start again.
This goes tripple for 'fixed turret shooting sections' with the worst offender being Dead Space.
Also, major pet peeve, Ashley wasn't in Mass Effect 2. I was equally pissed off that Wrex wasn't either but at least he got a full descent cameo and you could visit him on Tutchunka anytime you liked (even if he runs out of things to say eventually) but Ashley? My favorite female in the series to date and absolute canon Love Interest gets all of five minutes of air time, in a lousy cameo and then gets booted right out of the game altogether save for one EMAIL to acknowledge she even existed at all.
Essentially downgrading that entire romance subplot in the first game to the importance of any of the simple side quests that also only ever got an email.
Another recent pet peeve that started in Fable 3.... in game jobs. Seriously, I hate them. I can appreciate that you need money to buy important items or have enough to gain entrance to important locations in the game world, but there is no reason that doing so has to be so boring. I played the game to have FUN, sitting around for fifteen minutes waiting to be prompted on what button to press isn't FUN unless it's guitar hero.
While I'm here let me also express my distain for having smaller enemies start running around on the battlefield during boss fights. I first started noticing it in Batman: Arkham Asylum and now it is really getting on my nerves. If there's already a monster the size of the state of Hawaii breathing down on my neck, that should be enough. Don't then swarm me with a million henchmen as well.
Finally, why do there have to be so few matchmaking gametypes that accomodate elites in Halo: Reach? Seriously, I love playing as them but if I'm playing online I'll never be able to because the gametypes pop up very rarely and then get voted down and even in invasion I rarely get to the part where I get to play as an elite because my connection keeps dying.... actually come to think of it:
NUMBER ONE PET PEEVE:
MY CONNECTION KEEPS DROPPING OUT IN ONLINE GAMES!!!