Aeris was annoying and even painful - but it was meant to be.
FFVIII (which I've never finished, though do want to) - hmm... do I use my characters puny attack or do I summon an esper that will smack the bejeebus out of everyone?
Seriously, if I had been able to swap <attack> out for ANYTHING else, I think I would have done that with every character.
I find annoying plot points that require you to follow a specific hint that's only given once, or possibly not at all. I'm remembering FFIV (a great game). But when you leave the underworld (whatever they called it) Cid yells up to you to check with his guys. One playthough I forgot or missed that or something. I went all over the freaking world talking to everybody I could think of to try to get the plot to advance.
Another thing I find annoying is forcing the player to change playstyle midway through the game. Case in point - Vampire the Masquerade: Bloodlines. I love the game, especially modded, but it really suffers from this (in no small part because Activision rushed it out the door). In the beginning you can fight unarmed, melee, or use guns. Or you can be a "social" vampire and talk and mind-control your way through most of the quests. Then comes Chinatown - from that point on the game basically switches to a FPS. Guns are better than everything else, there are no more "social" options (there's hardly any more dialogue at all, honestly). So a player that was spending his XP for a certain style ends up gimped beyond belief at the drop of a hat, with absolutely no way to correct it other than cheat codes or restarting the game.