A big part of the wonder of DOTA 2 and games like it, and the reason behind their immense popularity, is the amount of itches they scratch.

They have a huge character roster with moves to master, like a fighting game.

They satisfy the need for blood and kills, and overwhelming your opponents, and bragging just like shooters.

They have social elements and cooperation, like MMOs.

And DOTA 2 EXCELS at all these, too. Why would I play Battlefield, or Skullgirls, or World of Warcraft when I have DOTA. All of these fields are invaded at once by DOTA and its peers.
It is one of the most complete and perfect online experiences. The only thing I need to satisfy my needs as a gamer other than DOTA are single player games, if I ever want to go online, to have some fun casually with my friends, or to just kick some ass and let off some steam, the best option is only one: DOTA.

And it's a game that rewards prolonged play and punishes the absence of practice, so if you want to play it SOMETIMES, you better play it ALL THE TIME, and I'm honestly fine with it, because of the "itches it can scratch."

The idea of a game divided in isolated matches where it doesn't matter what happened before or what will happen later, there is no constant character to grind until you reach level 300, you jump in, kick some ass, get out, all the while you learned how to move better, and maybe a few notions.

Shooters have been for a long time one of the only options for online multiplayer based mainly on reflexes, fighting games don't put you inside of a big crowd where you can stand out thanks to your skill, they are 1v1, same goes for rts games, they are usually 1v1, 2v2 experiences.

In shooters and in DOTA you enter a match and there's a bunch of unknown people around you, and if you perform well enough you can impress them, this can be a driving factor for some players and its one that exists here in this game.

Everytime I lose, I feel the need to win, and everytime I win, I feel like I need to win again: I can't stop playing this game.

This is the first time I've ever seen anything like this, in about 20 years of gaming. 100% free, extremely frequent updates, new content constantly (all still free), holiday events, The International, cool items that can drop for free, the trading system and steam market, semi-frequent balancing patches, and obvious evidence that they read feedback and apply it in a very short time. This just doesn't happen in other games.

The game is perfect, play it already.