The most annoying feature?

[BumblebeeCody]

^^^^^
Penance in FFX is insanely hard. Speedrunning the boss is considered to be within' the 30 minute range...

Zelda Skyward Sword: Fi (I really hate this character)
Zelda Skyward Sword: Motion+
Resident Evil 4: Ashley, at times, can be annoying. Especially if you're trying to run past enemies so she decided to duck and not move
Resident Evil 1&2 (@ SERIOUSLY THOUGH): Ink Ribbons!
Fighting games: Comeback mechanics (X-factor(!), Gems....)
JapaneseRPG: Generic Angsty Teenage characters who lack emotion like a Kristen Stewart film
Dead Rising 1: Dumbarse survivors

In general
Bad Checkpoints, horrible loading times, crap AI, game-breaking bugs (causing you to restart over), uskippable cutscenes, plot holes and I can't think of anymore right now.