Very interesting thread. My daughter (8 yo) just finished The Hobbit and is now reading LOTR. I'm re-reading any of my books that I'm passing on to her, so it's pushing me to keep reading quickly lol.
Ender's Game - in general I'd say this is a good book and I can't wait for her to read it, but she needs to be older. It deals with some older themes, especially bullying, and what Ender does (not the finale, but with Bonzo) would give her nightmares. If you've never read it, I'd suggest you reading it first before letting a 10 year old read it.
Belgariad - This is probably next on her list to read. I need to reread it (I haven't read the series in over a decade) but I think it should be plenty safe for a kid to read. I don't remember anything worse than LOTR.
Chronicles of Narnia - another one that should be fine at that age. I couldn't have been over 10 the first time I read it. I expect to introduce this to my daughter soon.
Myth - Fairly certain I read these when I was around that age. Thanks for the reminder, I'll have to look them up for my daughter.
Mushroom Planet - my daughter read the first one and enjoyed it, it's a scifi series from the 50s or so that was fairly innocent.
Tripods Trilogy - I read these when I was young and enjoyed them greatly.
EDIT:
Harry Potter - forgot to mention this at first, seemed like a no-brainer to me
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The first book at least should be easy, by the time it gets further along they are much darker, but still may be ok depending on maturity level.