Watership Down (classic book about rabbit adventures)
The All Creatures Great And Small series (about a British vet)
Anything in the Redwall series (about anthropomorphic animals that live in a medieval time)
Famous Five
Ship of Magic trilogy by Robin Hobb - but there is a sort-of sexual assault in the middle so you might like to read them first (bet you'll enjoy them, they're very good)
Solitaire Mystery by Jostein Gaarder - was given this when I was 10 or 11 and it is still my favourite book
Phantom Tollbooth - a little young but very good
Call of the Wild/White Fang
Day of the Triffids (a little scary but awesome)
The Cat Who... series by Lillian Jackson Braun (about a reporter/detective whose cats help him solve crimes and mysteries)
The Eragon series by Christopher Paolini
Anything by Robin Jarvis - Gothic mystery/slightly creepy stories (written for older children/young adults)
Stardust by Neil Gaiman (I adore this book)
Heidi
Anne of green gables
Alice in Wonderland / Through The Looking Glass
Dragon Keeper by Carole Wilkinson
Sophie's World by Jostein Gaarder - really, truly excellent book but could be a little heavy going for her age. I was given it age 8 but couldn't get all the way through without skipping any until about age 10.
Anything by CS Lewis - my favourite is Horse and His Boy
Clan of the Cave Bear and the rest of the series - but there is some sexual content so probably read it first
To kill a mockingbird
How Long Is A Piece Of String / Why Do Buses Come In Threes - books about the mathematics of everyday life (non-fiction but very enjoyable)
If I think of more I'll add them