I let my 5 year old watch animated superhero stuff, but I haven't let her watch any live-action yet. My mom thinks that's crazy, but I don't really want her to see people getting shot and stuff! (Or, I guess, seeing her mom bawl through parts of the Avengers might have been upsetting as well...)
The problem for M. is always the violence. For some reason, I'm ok with the animated violence but when it's real person on real person violence, I won't let her watch it yet.