the hilarious escort quests in world of warcraft where you get goodies for following a suicidal donkey around a camp of baddies. Beforementioned donkey is not concerned by the amount of health/mana you have and does not seem to realize his survival is depending on those amounts. There you are, out of mana and nearly out of health, trying to save a 'person' with the average IQ of a dead plant whilst he/she runs off into half a dozen baddies at the same time.
I generally grab those quests to watch them die and laugh, then I abandon them.
Secondly, the liquid frustration coming out my ears when I tried fable. I got this lovely skill turning me into a hulk-like figure with the ability to knock down every opponent in a single blow. However, once on the ground, I could not hit the enemies no matter what I did. I had to wait for them to get up, before I'd knock em down again. This, and the amounts of knocks it requires later on in the game to kill something gave an abundance of auto-cannibalistic frustration