Personally the thing that makes story games most fun for me to play is unique and interesting characters, as well as lots of character interaction. I also hate seeing cliche fantasy characters like the ones listed below:
1. Damsel in Distress: Like the others said, rescuing helpless princesses has been done to death. A regular girl who isn't a fearless warrior is fine, so long as she's intelligent or funny or cunning or... I don't know, just make her good at something other than waving her arms around screaming "Save me Popeye!"
2. Bitchy Warrior Princess: Even more cliche than the damsel in distress is the warrior woman who's a complete bitch for no apparent reason. They're the ones that go on about how they don't need no man to protect them, get attacked by bandits, have to be saved by the main character, and then yell at the main character for saving them and insist that they could've done it themselves.
3. Knights in Shining Armor: The perfect hero who fights for justice and freedom and truth and love and has absolutely no faults whatsoever... Just no.
4. The Orphan Farm Boy: He lived happily on his little farm with his mother and father until the evil overlord attacked his farm, murdered his parents and left the boy alive for no particular reason. He got taken in by a wise old wizard who raised him as his own, and now that the boy's reached his sixteenth birthday, he's old enough to go out and seek revenge! It's been done... A LOT.
5. The Bumbling Dwarf: He drinks, he curses, he burps, he farts, he falls over a lot and he's just in the story for comic relief. Why does nobody make a drunk, bumbling elf? That'd be awesome!
6. The Pointless Elf: He's an elf... And... That's it. He has no personality and never really does or says anything useful or witty or wise, he's just there because your group needs an elf in it.
7. The Evil Villain of Death and Evilness: He wants to destroy the world!!! No reason, he just likes destroying things.