Dragon Ball is perfect if she likes Shonen
I might let a ten year old watch Naruto and I might let them watch Bleach, but they can be bloody and Bleach may be frighting, she may prefer to start on Shoujo and Dragon Ball if she is a bit squeamish with violence
Ranma, Tenchi, Outlaw Star, (maybe) obviously Pokemon and Yugioh, Sailor Moon, fruits basket, (perfect if she likes shoujo).
I would not let her watch Evengelion until she is at least thirteen
A good meet in the middle is The Mysterious Cities of Gold, it was my introduction to Anime, although I believe it was made for the western market.
What about Hack? I only ever saw a few episodes but never saw anything unsuitable