Are there any games like League of Legends

DotA (Defense of The Ancients) is the game that originated LoL. It's very similar.Try it.

Other than those, there are also the following:

Heroes of Newerth (HoN): stays more true to DoTa than LoL. Recently became Free-2-Play.

Dota 2: Technically not out yet, but due november this year I believe (or was it next year? Anyway, it's valve time)

Demigod: A forgotten game, but should mention it I guess. Didn't quite get the concept right in my opinion.