Desert Punk.

Okay, serieous suggestions now.

Bleach is a pretty good one. It's got good action and a decent story that's easy to understand, and doesn't treat you like an idiot. It's got some pretty terrible pacing, but I don't think that will bother an 11 year old.

Law of Ueki is a pretty safe bet. It's fun, the fights are imaginative, and it keeps itself fairly fresh through out all it's 54 or so episodes. Theres a few head scratching moments, like the shows inability to due math, but on a whole it's enjoyable enough.

As far as movies, Origin is a pretty solid movie. It's overal style is similar to that of Miyazaki, though it's done by someone else. It's a bit preachier them Miyazaki, but pleasant enough regardless of that.

I'd suggest Cowbowy Bebop, while it's targeted a bit older then 11, it's an absolutely wonderful show, and there's plenty in it for a younger audience, as well as being an amazing show all around. I forget which episode, but if you have the DVD version one episode you see a guy looking at a porn mag, and you see boobs, so you may want to screen it for that episode, but it only happens once.