Well, that's a question that will have lots of anwers I suppose
First, because of her talent, obviously! I feel like she can play anything she wants! Bob Dylan, Elizabeth the 1st, a russian agent in "Indiana Jones", Katharine Hepburn, and so many others... The characters are so different from each other! She's not like the actresses who stay in the comedy-genre and just play superficial chicks!
Also the emotion that she can show on screen is very real. Sometimes when I watch her, I'm not even thinking that she's acting
I suppose this comes for her theatre experience
Then she seems to be such a simple, down-to-earth and nice woman. Remember her reaction when Marion Cotillard won the Oscar? She's never in a competition... Or maybe only with herself, and that's what everyone should do! She seems to be so clever too! I love to listen to her talking
And finally, the fact that she cares for her country (the environment, etc...), that she doesn't want to stay in Hollywood, that she's not followed by paparazzis all the time...
Oh and so many other reasons that I can't find right now!!!
Cate is amazing