Hmm. I'm inclined to say boxelders simply because they have been the most bothersome as of late, but on the whole they're slow, dumb, and don't actually do much, so it'd seem a waste. Really, I feel at this point that mosquitoes need to go the most. Minnesota can find a new state bird.
Y'know, TotalBiscuit would immediately say Brothers: A Tale of Two Sons, but I have to admit that I never really got as much out of it as he clearly did.
The TellTale games of late have done well, but they're so full of objectionable content.
The Deus Ex games have, as a whole, done well, but I don't feel they do anything terribly unique in terms of how they told the story.
There's definitely something to be said for the Half-Life/Portal series with the distinct lack of cutscenes and hiding the deeper story elements throughout the environment for you to discover, but it's really only a step or so above other games.
I could list all kinds of games that have amazing stories (To the Moon, Darksiders, BioShock Infinite, Dust: An Elysian Tail, KOTOR/TSL, Beyond Good & Evil), but the act of it being told in a game instead of some other medium rarely adds a whole lot.
Can I just get Cosmic Star Heroine now? Pleeease?