League of Legends. There is a reason it's one of the most popular PC games around currently. Very fun, very addicting, and VERY rewarding. Best of all, it's free!
Keep in mind that it has a HUGE learning curve (second only to something like Starcraft, in my opinion). I've won a bit over 300 games. Assuming an average 50/50 win to loss ratio, that puts me at around 600 games. Each game averages around 30-45 minutes. That's a LOT of time to put into a game, and I still have a lot to learn and improve on!
If you get into it, you should expect the game to be initially frustrating, annoying, confusing, not fun, and you should expect to feel like you're an awful player often. After many, many long hours of playing, you'll begin to see some sun shining through the clouds. Once you pick up some solid skills and move up into higher levels, everything should just click. Most people that start it have a hard time getting into it, but find they can't give it up once they play enough.
Also, the community can be awful, but not always. My advice is to focus on having fun instead of winning. Of course, do your best and TRY to win, but don't get yourself down if you or your team does poorly. There are a bunch of assholes on LoL, but it doesn't really bother me. Some people rage no matter what. Some people rage because someone is genuinely doing something wrong. I don't think it's a good thing to rage over someone's performance, but many times these players do have good advice hidden under their angry words.
It doesn't require an extremely beefy computer to run well at low settings, so almost anyone with a modern computer can play it.
I never played the original DOTA and have yet to try DOTA 2, but I hated Heroes of Newerth. Yeah, the graphics are technically better, but the art style made it hard to tell what was going on. I hated the pacing. The characters all seemed to be bland and vague. The interface is just horrible and confusing, and I had no idea what was going on when trying to start a game, pick characters to play, etc. In game, the interface is fine. LoL might not be as "hardcore" as HoN, but it just feels better overall. It is more fun and user friendly. It is much easier to pick up, play, and generally understand what is going on in the game (and any interfaces leading up to the game itself). It's no skin off my back if someone prefers HoN, but I thought it was garbage compared to LoL.