I'd like to do something epic and cinematic. I created a sheet for a character Solomon Stormtooth who would have been in a plane-hopping game, but I didn't get chosen. Dwarf with two magic axes, rakish personality, it would have been fun. But that kind of interstellar/planar voyaging really appeals to me. A space opera type feel.
Something really gritty is always fun, but it has to be done right. Everybody wants to do gritty, except I feel like a lot of times people miss the point: in a gritty campaign, PCs can't be skewed to live, they need to be just as susceptible to death as every average Joe. Way increased hit points and stuff like that doesn't fit in with it. A gritty fantasy setting would be incredible if it could be pulled off right, but gritty tends to pull one way and fantasy in the opposite. If the dragon's breath can melt your shield, it makes it tough to want to fight dragons. But then, circumstances don't always skew to what you want to do, and that's where the fun would lie.
Mostly, I want to play a game where my actions (and those of the party) are, for the most part, unrestricted. Without pre-set campaigns, that is. It would require a creative GM, definitely, but I think that kind of campaign would be the most fun for all involved.