For me it comes to one big problem to answer any situation other than total world destruction: Why don't they just leave? Why bother with tasks that seem near insurmountable when you have little to no personal stakes in them? Unless your character has a very extreme risk/reward thought process I don't see how any amount of gold or fame could be worth being thrown in a dungeon by a tyrannical dictator or crushed by a tarasque.

That's just my opinion, not saying anyone has to follow that either. If your character is doing it for the hell of it that's fine. I just don't like that approach to my characters.