Smite is my go-to for when I'm burned out on the tension of LOL and I just want to kill people. They have a Summoner's Rift clone map, but they also have 5 or 6 other modes of varying degrees of deathmatchiness, and they also beat LOL to the limited time goofy game style of the day concept. Awesomenauts is also in this vein- goofy fun, with the distinction of being the only 2D MOBA I know of. They have a big expansion in the works as well, which will add a lot once it's complete.
DOTA is the obvious choice if you're serious about your MOBAs. Its skill designs and itemization options are more bizarre and interesting than LOL, and people with good micro skills can do amazing things with the ability to control multiple units, but there are some divisive aspects of the game (unreliable gold, denying, the courier) that make it harder to get into the game and that require more consistently good play out of you in order to succeed. If you do get into it though, they just added ability draft mode, which is a blast.
Beyond that, you can try to get into the Infinite Crisis beta, which is only OK at this point. The only other MOBAs I've played are Heroes of Newerth and Guardians of Middle Earth, and I wouldn't recommend either of them.