League of Legends is the most interesting game I've seen in awhile that I knew nothing about. It's the successor to the Defense of the Ancients map, itself a sort of logical continuation of what Warcraft 3 did in adding heroes to RTS games. Only with a tower defense spin. And it's a really interesting, complex game. But I get ahead of myself.
In LoL you play a Champion, a little dude who runs around and kills monsters and enemy champions. The map you play on is a tower defense style map, with several lanes from one end to the other you fight your way down. Lanes are protected by towers, and also waves of little creep mobs spawn on occasion and run down the lanes. The map is symmetric and it's very much a PvP game: your champion, towers, and creeps vs. the enemies.
What's neat is the game has a nice rhythm to it, an ebb and flow as each side presses the advantage. Also it has a bunch of really complex theorycrafting underneath it. I've barely scratched the surface but it's clear that a bit of research can give a player an advantage.
LoL is free to play. You can spend money for various boosts, mostly increases in how fast you earn experience. I can't quite tell if any of the for-pay options give you a competitive edge in PvP. I think not, but I'm not positive.