Story, Quality, enjoyment, laughter, relation, and more. People enjoy anime just like why they enjoy movies or TV shows. Sometimes even more because they fell that they can connect better or that its just something they enjoy more.
I just like cartoons, better than watching a well known actor whos' been in several movies to wreck the reality of it all. Besides, If I had to back Chuck Norris or Optimus Prime, I'd be a prime fan even if we'd loose!
For me, It's a chance to escape reality, Experience what it's like to jump from a mountain and not get a scratch. But yes, It gives me a chance to escape from my boring reality. Same goes for games.