Somewhere between picture books and chapter books, there is a category that's not totally named. If you go to your local bookstore, they probably have bright numbers on certain books like "Step 1 Reading" or the like. But I find that there are better ones out there. Here is a list of books and/or authors who have chapter books that are heavily illustrated so they're great for those kids who want to step out of picture books but find chapter books just a bit too daunting...
And as a side note, you might check your library for "Jim Trelease's Read Aloud Handbook" - this is a book full of reviews about children's books. He reviews the storyline, tells you what age would like it, how it's illustrated, etc. I've gotten a lot of good ideas out of that one.
The Cynthia Rylant books (Mr. Putter and Tabby)
Magic Tree House series
Beatrix Potter books
Alice in Wonderland (Try the one illustrated by Alison Jay, "Alice's Adventures in Wonderland.")
Marguerite Henry's books
Beverly Cleary books
Jigsaw Jones mysteries
Nate the Great series
Pixie Tricks series
Rainbow Fairies and Weather Fairies
Barbara Cooney books
Brian Wildsmith books
Ramona Quimby series
Bunnicula Tales (which is an early reader form of the Bunnicula books)
Amelia Bedelia books (for homeschoolers, this is heavily centered in school)
Junie B Jones books (for homeschoolers, this is heavily centered in school)
Little House books, I believe, have younger versions.
I've heard the Incredible Journey books are great - and just might spin you off into studying geography or history too. :) ijbooks.com
The series by Gerinomo Stilton - I just found these myself and they're *very cute* and lots of colorful small pics throughout the books (20+). You can view a few pages on Amazon.
And don't forget comic books and graphic novels!!! Like Peanuts, Bone, Garfield, etc.
For a little bit older (or if you are reading to him/her), there's a really great series by Bill Myers (he co-wrote the McGee and Me series if you're familiar with that). It's very funny Christian stories for kids. Both my newly 8yr old son *and* I have been howling reading the series. We're on "My Life As Reindeer Roadkill" right now - a great Christmas story where the main character gets invited to Jesus' bday party by an angel in a dream. He spends a while trying to determine if it was real...and if it was, what in kind of a birthday gift could you get for the Son of God??? It's an older series but if you have a big church, it might be in their library.
I googled "early reader chapter books" and some good lists hanging around. You might try that too. Here's one that looked good http://www.bellaonline.com/subjects/10465.asp
If you have any to add to my list, please add it in the comments!