I watch a lot of Dota 2 on Twitch because I find it to be a pretty interesting game to spectate. Also, it's a good way to learn the game. I don't watch much else in terms of Let's Plays and streams, except Jeff Green (cause he's fun as hell) and the occasional GB staff stream.
I mostly watch Draskyl on Twitch. Pretty knowledgeable and skilled at Dota. Also, I like his personality and the people he plays with. And he has good taste in music.
I don't think there's a simple answer to why we watch other people play games rather than play them ourselves. It all depends on what you want out of it.
Edit: Draskyl and crew http://www.twitch.tv/draskyl/b/535714518