I haven't read all the replies, but we've read Stuart Little, and I felt there was quite a bit in that one that needed edited. As I'm reading aloud, I just change the words a bit, and skip over parts, and dd doesn't even seem to notice. But, I did want to give the heads up. I'm not interested in introducing boy meets girl to my 3 or 4 year old!
With a little editing here and there, dd has really enjoyed the Childhood of Famous Americans series. We tend to like the ones written by Augusta Stevenson the best, but they are all good. At 3, she was Abe Lincoln for WEEKS, feeding a soldier a fish she'd caught with her hands.

We've also enjoyed the Little House books and read up until the school meanness with Nellie starts in full force. I think she's heard the first 4 or 5 books.
If you are Christian, the In Grandma's Attic series is wonderful.
We liked Charlie and Chocolate Factory, though I did edit some of that, too.
It seems like at 3, maybe more at 2, dd also really enjoyed the Little Animal books. They aren't very long, and include lots of photographs, but they are real stories. (the Little Puppy, The Little Kitten, The Little Duck, etc. I think there are 6 in all.)
The original Winnie the Pooh is good, as is the original Curious George series.
We LOVE Dr. Suess here, too. A lot of his bigger books pack a good lesson, too. The Sneetches, for example.
Virginia Burton (Mike Mulligan and the Steam Shovel and other stories) is good. Longer stories, fewer pictures, good plot.
Dd also loves Robert McCloskey's books. One Morning in Maine, Make Way for Ducklings, Blueberries for Sal. Their realness seems to speak to her.
You could go to amblesideonline.org and check out their books lists for year 0 and year 1. There are lots and lots of suggestions of classic books to share with littles.