This is somewhat belated, but a couple of weeks ago I GM'd for a unique role-playing game. One of my friends +Aisha Cruse has been going on a You Tube chronicled resolution binge this year, attempting all sorts of novel activities. One of her resolutions was to play a table-top RPG. Cue me.
+Matthew McComb suggested Mouseguard, which I think is a great choice for a first time RPG experience. The game, based on a comic by David Petersen of the same name, allows players to become a mouse warrior in service of a paramilitary organization protecting the mouse territories. Basically, in Mouseguard, you get to play mice armed with swords. This would all be very cute if it wasn't for the superior production quality of the book (seriously this is the best looking RPG I've ever seen) and the fact the rules were written by Luke Crane of Burning Wheel fame. The basic mechanics of the game, earning passes and fails on skill checks to simulate the slow increase of abilities, team-based conflicts, all work ridiculously well together. I explain this a little bit more in the video so check it out: