I enjoy anime for the unique and deep story lines it offers, I also love (most) of the characters some of them have inspired me in my life to do things I never would have done without them. Then there is the artwork I love the anime style of drawing and really wish I could do it myself (I do try).
Another reason would be due to the fact I can't get on very well with real people and find it difficult to feel much during my daily life yet while I'm watching anime I can cry, get angry, be shocked, smile, laugh, regret and get excited with the characters there is a bond there that I can't develop with real people (I suppose it's much like how someone can get attached to a book or TV character)
In every anime I watch I learn something new about people, about morals, about life and of course I learn about Japan too. I feel completely involved in every anime even though I'm sat on my bed I yell encouragement and warn them of danger, just sitting there can give me the most amazing feelings some I never knew I could feel until I started watched anime. There are so many more reasons why I love anime (like the music) but I think to me these are the important points, to me anime is friend I never had and I do believe that without it I'd be far more messed up than I am now.
This Image could also partly sum it up