Some good recommendations here. I'll add:
Two old series I loved as a kid. The first books of each at least held up to my kids
The Prydain Chronicles, by Lloyd Alexander
The Dark Is Rising Series, by Susan Cooper
Some more recent series:
The Spirit Animals series is very kid friendly. Even though there are multiple authors the consistency is pretty good.
The Heroes Guide to saving Your Kingdom, by Christopher Healy is the first book in a series that is a humorous romp through fairytales.
And a recent stand alone book I liked:
The Night Fairy, by Laura Amy Schlitz
Hmm. Some of those sound a little advanced for a four year old.
If they like the Lion, the witch and the wardrobe you've got the rest of the Chronicles of Narnia - I bought the boxed set for my nephews, and now they've stopped reading to my grand niece (she's teenaging, and my grandnephew was one this week, so is not yet very word profound. I lover TH White's 'The sword in the stone', niece's copy of Watership Down is totally loose leaf by now (I don't think the original binding was very solid) and I had a grandfather who was very 'animal inclined', so I was read the Gerald Durrell books from very early, and loved them but that might have been the performance as much as the (rather grown up) content and humour.
Perhaps the Alice books? I know they're now being rejected for Freudian elements, but I was never upset by them.
Do they have any special likes? I remember my slightly younger grandniece being ready to accept anything with horses in it, and was being read 'Black Beauty' incredibly early (Mind, I was brought up by siamese cats, so was wild about a book called 'Tai Lu talking', which nobody else has ever heard of).
Talking Animal fantasies are more age appropriate if your kids like animals. They thrilled me as a child with their get-in-the-heads-of-animals imagination stretch often associated with fantasy and sci fi.
Charlotte's Web, by E.B. White
Mrs. Frisby and the Rats of NIMH, by Robert C. O'Brien
One Hundred and One Dalmatians, by Dodie Smith (I was just today strongly reminded of
the dog's Twilight Bark while listening to Terry Pratchet's Long Earth War and the
troll's long call.)
The Jungle Book, by Rudyard Kipling
Watership Down, by Richard Adams was not originally written for kids, but has been enjoyed by many of them.
Inkspell, Inkheart, and Inkdeath are good fantasy books that would be age appropriate. The author is Cornillia Funke (I may have misspelled her first name). They were some if my favorites when I was younger, particularly the second one Inkspell.