Not that I’ve played many games in the past few years and I’m a Chaosium Call of Cthulhu fan myself (and the BRP mechanics in general) but if you want a rules-light game that emphasizes narrative and role-playing, I think FATE system is one of the best, and both the Core (complete) and Accelerated (quick) rule sets are available online for free; all you need are some six-sided dice. (You can—and should—buy FUDGE dice but you can use normal six sided dice and just remember that 1-2 is -1, 3-4 is 0, and 5-6 is +1). The system is rules are genre-independent although there are games with specific rules for their setting, such as Spirit of the Century, and because of the streamlined rules and quick character generation it is ideal for a quick pickup game where you just want to play through a single scenario. Here is a Tabletop episode of playing a pickup scenario using FATE Core. One of the best things about the game is that it gives the players some considerable freedom to influence the action by using Aspects and Fate Points. This can seem a little daunting at first to both the GM and players because in a good game the players have to actively participate in the narrative rather than just responding to whatever the GM throws at them, but a good collaboration between GM and players can really bump up the storytelling to another level.
I’ve never played it but Monte Cook’s Cypher System is supposed to be rules light and fast playing. Numenara, the first game published using that system, got a lot of great reviews.
If you actually want a purely narrative game with no GM or mechanics other than some die rolling to pick plot points, Fiasco can be a lot of fun, although it does take a creative group which are all on the same wavelength regarding the sensibility of the game. If you go into it with half the people thinking of a Coen Bros. film and the other half trying to play a Jane Austen story—well, that actually might be a lot of fun, although someone is probably going to end up in tears. Anyway, that’s another game that only requires six-sided dice, although you are going to need a bunch of them.
Or, if you just want to kill some people quickly, Machine of Death offers some quick sort-of-roleplaying under time pressure; basically, given a way the target is predicted to die, you have to arrange for their death in often improbable ways. It doesn’t lend itself to extended play but is good for a quick pickup, or to take a break from more intense game playing.