Lately I've become very familiar with a certain type of book: the illustrated early chapter book. I'm happy to see more and more books of this sort becoming available. Everybody's different, and I know what appeals to my kids may not appeal to others, but here are some of the titles that worked as early transition books from picture books to chapters.
The Dragon Masters series written by Tracey West and illustrated by Graham Howells. Dragons, adventure. This is a good one. Both my son and daughter enjoyed it. http://www.scholastic.com/branches/dragons.htm
The 13-Story Treehouse written by Andy Griffiths and illustrated by Terry Denton. Funny, silly, terrific. There are more, if your kid likes it! http://us.macmillan.com/the13storytreehouse/andygriffiths
The Gumazing Gum Girl: Chews Your Destiny written and illustrated by Rhode Montijo. Superheroes and bubble gum. My kids read it more than once. https://www.amazon.com/Gumazing-Girl-Chews-Destiny-Novel/dp/1423157400
Tales of Bunjitsu Bunny written and illustrated by John Himmelman. I personally enjoyed these stories. One included a paper-folding craft to make a Bunjitsu Bunny. It was easy enough even for me and my 5 year old. http://us.macmillan.com/talesofbunjitsubunny/johnhimmelman
Princess Pink and the Land of Fake-Believe by Noah Z. Jones. Funny fairy-tales very unlike the classics. For example, the first book is entitled, "Moldylocks and the Three Beards." You heard me. http://www.scholastic.com/branches/princesspink.htm
Finally, I want to plug my all time favorite book to read aloud to the kids. My Father's Dragon. I recommend getting the book this minute for story time tonight. http://www.scholastic.com/teachers/book/my-fathers-dragon#cart/cleanup