I would if I thought at least one of them actually had a chance. The thing is I know none of them do.
"They taste like.burning!"

Surely, and especially in the case of Batman.
Batman is a character much more interesting than his "villains". Even because most of them are ridiculously bizarre and absurd (I mean, Mr Freeze? Poison Ivy? Riddler? Mad Hatter?, are such characters really more interesting than Batman, with all his abilities and his complex personality?)
I really don't think so.
Now, there are some heroes I couldn't care less about (Spider-Man, Superman, Wonder Woman), but even in such cases, their villains are even less interesting than themselves, with the possible exception of Lex Luthor (the archenemy of Superman).

Yes. Let's go along with the Batman example. As awesome as a villain like Ledger's Joker or Hardy's Bane may be, my favorite character is still Batman. The closest thing to an exception would be Frank Gorshin's Riddler.

A hero is defined by the villain. The better the villain, the more the hero shines. That beings said, of course I root for the hero.
In the kingdom of the blind, you're the village idiot.

Yes, I root for the heroes. Imagine these things really happening. Though colorful, many of the villains are also total ***holes who you would not want to terrorize you.

No. Or rather, I'm sure there are some people who do, but I'm not one of them.
The villains are more colorful, entertaining and complex, I think, and that's what makes them interesting. Does anyone else feel the same way?
edit for clarification