League of Legends is a real time strategy game based on the user created map Defense of the Ancients for Warcraft III. The basic idea is you control a single unit in a large battle with the eventual goal of destroying your opponent's home base. An individual game lasts for about 20-60 minutes and your champion starts each game at level 1. You spend the early game accumulating experience and gold which allows your champion to learn new skills and buy better gear. Eventually you start trying to kill opposing champions (bonus experience, bonus gold, and they can't play for a short time while they respawn giving your team a tactical advantage) or trying to permanently destroy defensive structures in an attempt to win the game. Each side has 5 player controlled champions and repeated waves of computer controlled trash mobs. With 74 different champions each having 5 skills and a huge number of items to buy the game has a lot of replayability just trying different things nevermind actually trying to be awesome as a team.
It's also free to play. Well, in a sense. LoL has completely embraced the concept of micro-transactions and built an entire meta-game around the individual game. There are 74 champions in the game but only 10 are available at any given time for free play. (The 10 change every week and seem to always have a good mix of tanks, support, melee, and mages.) Want to play a hero that isn't free? Well, you can pay some money and permanently buy the ability to play as that character. They've also built a level-up system for players so that each time you play a game your champions get a little better. You get talent trees and glyphs to modify your characters so even if two people are playing the same champion they could function differently if one talented into the defensive tree and one in the offensive tree. Talents are free but glyphs you need to buy with an in game currency that you earn as you play games. Or, perhaps, spend some real money to get more glyphs too. You can spend money on buffs to increase how fast you gain player experience.
A free player will get to max player level slower than someone who pays but eventually when they get there they'll have the same power as someone who pays a lot of money. The free player will have limited options each week on who they can play and probably only has one set of glyphs so they're only really optimal with one type of character instead of with all characters but when it comes right down to it a good free player will beat a mediocre paid player every time.
This is the kind of micro-transaction of which I approve. Games need to be paid for somehow and the people paying here aren't getting much of an advantage for their money. They're getting different skins for their champions and getting more flexibility and have to spend less time to level up, sure, but nothing earth shattering. I should note here that there is a match-making system when you sign up as 1 person in a 5v5 match such that the teams are fairly balanced so being a lower level won't mean you just get stomped every game. It means you'll just keep playing other low leveled people or maybe you'll get a high level dude on your team too.
It's a really fun game with lots of different numbers that get bigger both in an individual game and in the external meta-game. Being free of the WC3 engine meant some things changed significantly from DotA but a lot of what they did just feels right. (By contrast another DotA clone, Heroes of Newerth, was not nearly as fun as DotA was. LoL may actually be more fun.)