Which enemies annoy you to no end? Any non-boss enemy from any non-mmo FF game counts.
I'm gonna have to go with any kind of Malboro or other status-effect nightmare enemy. The enemies themselves are rarely that bad but the status effects they put on you are such a pain in the a** to get rid of. I also hate Flans and their ilk, because I don't like being forced to use magic (i'm a physical-attack oriented player), especially when i have to guess which type of spell i have to use.