I haven't run anything with this of late, but I do rather love the Apocalypse World system and all the variations I've read so far.
Players have a list of basic moves, plus some additional moves specific to their character type, that they can roll two six-sided dice on, adding one of their stats to the roll. 10+ is a great success, 7-9 is a partial success and below 6 is a failure. Depending on the move, there will be specific things that happen on successes, partials and failures. As the GM, you never have to roll but you have your own more varied list of moves to choose from, some of which are deemed 'hard moves' which you can choose to invoke if a player fails a roll. Whatever move you choose, that's what happens next and then the players react to that with their own moves and so on.
It sounds very limiting in theory, but in practice there's room for interpretation about a move's outcome. The system makes improvised play a lot easier, because it gives you guidance as to where to take your shared story next. The way character creation works in most of these games also ensures that all player characters have ties to one another, which is handy - especially for one-shots - to get things rolling quicker.
I have yet to play Apocalypse World itself - to be honest, I'm much more interested in playing a game of Apocalypse World than running one - but I've run a number of different sessions of Monster of the Week. I also have Dungeon World, which I mean to try one of these days, and - although I don't have them myself - I'd like to give Monsterhearts and the recently kickstarted Urban Shadows a try as a player as well.