My Neighbor Totoro is an awesome movie. It seems like it's designed for kids (and maybe it is), but it's something most people could enjoy, I think.
I recommend watching with Japanese audio and English subtitles (though the English ones work well enough—I prefer it for cultural reasons). I should note, however, that the kids are louder when they scream, in Japanese (though they're probably quieter the rest of the time). There are probably more religious aspects to the movie with the Japanese, though, if that bothers you. The characters express different emotions, attitudes and sentiments in both versions (I prefer the Japanese).
I'm not sure if the idea of a totoro is a Miyazaki / Studio Ghibli invention or something else. They talk about them like they're things from a story book (which book I suppose could have been pre-existing; I'd like to know, if so). Apparently, all three of the creatures are totoros, although they really only call the big one Totoro to its face. I wonder if totoro is a word for troll in Japanese (I think they call the thing from the story book a troll once).
The movie is quite amusing, due to the characters, though I wouldn't call it an outright comedy.
There isn't any violence. I would be surprised if it isn't rated G.
The animation's not bad, actually, although it was probably better in Spirited Away, Whisper of the Heart and Howl's Moving Castle.
All in all, it's a great film. I got it from my local library, in the children's section (they put the animé there for some reason—although I think this one fits quite well).