The usual Star Wars gang tried something new last weekend -- Dungeon World. I was impressed. While it has the trappings of older D&D-style games, Dungeon World uses some interesting bite-sized mechanics called "moves" that streamline play. You can hunt up the official page for yourself, but since it's based on OGL content, a lot of it is online for free.
It's a simple game. Not as bare-bones as the original Gnomemurdered!, which still sets the standard for ease of play, but you could teach it to your eight-year-old kid or your fortysomething-friend-who-hasn't-roleplayed-much. Character generation is basically a flowchart. The idea of moves makes it easy for players to decide on their actions. Its skeleton is D&D, so it's a snap to pick up if you know that game already.
Dungeon World also buys into some of the things I don't want in a game. Classes? Yes. Hit points? Yes (although I don't think they increase with experience, which is a plus). Halflings? Yes. Railroading PCs down specific stereotypical developmental tracks? Yes.
I haven't looked over the GM rules carefully yet. They have a weird storygame vibe, but they might also make the play experience more fun.
I think you could easily fix most of the things I don't like --f'rinstance, make the list of starting moves open to all new PCs, to get rid of that musty 1970s smell. It's simple and modular enough to accommodate that. Dungeon World looks like a solid little game that's worth your attention.