I love reading chapter books to my boys. I have had success introducing chapter books to my very different sons at around 3 and a half, and I find it improves their attention span, vocabulary, and ability to narrate their own stories. Of course we still read plenty of picture books too.
It can be difficult to choose books for this age because many easier chapter books which might appeal to them are written for older children, and therefore indulge in highly idiomatic language and/ or rude or disrespectful dialogue. In our TV free house, my kids are very sensitive to violence and "mean" behavior, and I also search for books which limit these qualities. The books on this list are, I think, appropriately innocent and sweet, with some noted exceptions.
The books below are generally listed in order of complexity. The first books on the list were read to my children before they turned 4. Some books written for early readers are great choices to start your child on chapter books, because they work so hard at holding young children's interest from chapter to chapter. They also tend to have more pictures to help children transition from picture books. My older son (now 7 and an avid early reader) has returned to many of these books to read them independently.
Magic Tree House Boxed Set, Books 1-28 I read this entire series to my sons when they were between three and four. This is a great early series, with a lot of adventure and interesting content but simple language and short chapters. The stories really help generate interest in the history and natural history covered in the books, and we read a lot of follow up picture books which explored their interests further.
Three Tales of My Father's Dragon All three of these stories are page turning adventures which held my children's interests when they were younger than 4. These books are fun for adults too.
Catwings (A Catwings Tale) My kids found this series about cats with wings very appealing. The books are short and simple, with many pictures.
Babe The Gallant Pig All of the books by Dick King Smith are sweet and simple enough for kids 3.5 or above, but this is our favorite. This book is superior to Charlotte's Web, in my opinion.
Little House in the Big Woods 75th Anniversary Edition This is the first book in the Little House Series, and it chronicles Laura's life in Wisconsin when she was four. The book is very simple and episodic, without a lot of action, but it does a good job helping a young child imagine life in "the old days," and leads to a lot of great discussions. It is a great book for kids as young as 3.5, but YMMV. My oldest son liked this a lot more than my middle son.
On The Banks Of Plum Creek I choose to skip over Little House on the Prairie (which is riddled with negative and stereotypical depictions of Native Americans), and move straight to this book, which is a lot more exciting than The Little House in the Big Woods. Your young child may find it hard to deal with or understand the motivation for Nancy's bullyish behavior, but the rest of the book is sweet and exciting for boys or girls 4 and up.
Pippi Longstocking (Puffin Modern Classics) Pippi is so spunky and lovable, what kid couldn't love her? She lives a child's dream: independent, rich, missing Pirate Father and a monkey and a horse living IN the house. My kids, especially my oldest, loves that she never does what the adults want or expect, and yet she isn't "fresh" or rude about it. This is my favorite book of the series.
The Giants and the Joneses This book turns Jack and the Beanstalk on its head, telling everything from both a Giant's and a "Iggly Plop's" perspective. The book is witty and sweet, and the giants only speak giant language, which kids have to figure out based on the context. Very fun.
Chitty Chitty Bang Bang This is another book I can't believe I didn't read as a child. The story is so exciting, involving a flying car (of course), robbers, a kidnapping, and an explosion, without being scary or too violent (IMO). I do really wish we hadn't watched the movie as a follow up, though. The movie is awful, and nothing like the book.
Stuart Little My middle son really enjoyed this book (more than I did). While I don't really understand the appeal of E.B. White's books, my kids sure seem to enjoy them. And his interest led us to read a series of mouse books.
The Mouse and the Motorcycle My middle son really enjoyed all three of the books in this series. This series really is written for an older child, and many of the character's circumstances and adventures (divorced parents, adventures in school and camp) are really beyond the experience of most 4 year olds, but they can't resist a talking mouse who can ride a toy motorcycle.
Poppy (Tales from Dimwood Forest)This is a fantastic book. A fabulous read for adults and children. And in the first chapter, a mouse character is killed by an owl. If your child can get beyond that, they will enjoy this book immensely. My only problem with this novel is the language used by the porcupine character. The porcupine is gruff and growly and "swears" with ridiculous terms like "dormouse dung" quite freqently. This becomes more of a problem in future books in the series. If I could do it over again, I would only read this book (instead of the whole series) to my kids.
Travels of Thelonious (The Fog Mound) This is a recent discovery, and this entire series is fabulous. The story takes place in a future post-human earth with talking animals with opposable thumbs, and alternates between written and graphic chapters. While the post-human earth element might sound scary, it isn't, and it really works as a read-aloud for my 4.5 year old and my 7.5 year old together.
The Complete Tales of Winnie-the-Pooh I was surprised how much my kids like these books. I find them a little dry compared to many books on this list, but my two oldest both liked these as 4 year olds.
The One-Eyed Giant (Odyssey) Mary Pope Osborne breaks Homer's Odyssey up into six separate easy-reading books so successfully, I am stunned they are not more popular. My oldest loved this series at 4, but I have yet to entice my middle son with them.
The Tale of the Despereaux My second son has been on quite a mouse kick. While this book contains some mature themes, including child abandonment, abuse (ear-boxing to the point of deafness) and parents who vote to send their son to his death because he won't conform, neither of my children found the book upsetting. The story is told very well, and fun for adults to read as well.
Arabel's Raven (Arabel and Mortimer) This story is goofy and quirky - a laugh out loud book which was just right for my jubilant middle son - which was not at all what I expected from this fantastic author of dark gothic novels.
Half Magic I am so glad I followed a friend's recommendation and introduced my kids to this book. My older son read it on his own, and loved it, and it was quite a hit with the 4 year old as a read-aloud. Written in the 1950's, with a clear bow to E. Nesbit's earlier magical adventures, Edward Eager places four very believable and likable sibilings into fun magical adventures. We will definitely read more of his books.