So I was going to mention some books that the kids (age 3-4.5) really like and then I realized that a lot of them featured pigs as protagonists. So here they are:
The Poppleton series by Cynthia Rylant, illustrated by Mark Teague. These are short chapter books that are quite funny, and the kids get the jokes, some of them silly tricks that the characters play on each other (is that a wart?). Mostly they are about Poppleton, a pig who moves to a small town and has gentle adventures with his friends and neighbors.
If you like the way Teague draws pigs, by the way, you should check out his book Pigsty.
Mr. & Mrs. Pig's Night Out and others by Mary Rayner. These books are out of print, but I found them in the library. The first book tells the story of what happens when the Pig parents get a babysitter who is a wolf. The sequels deal with the family band, an ice cream truck, too much ketchup and other vexing situations.
The Amazing Bone by William Steig. The classic about a pig who finds a talking bone.
Hog Eye by Susan Meddaugh. Illustrated in a style reminiscent of Steig, this book is told by a clever girl pig. She gets captured by a wolf, but because she can read and the wolf can't, she has the upper hand. The first time we read this, Austin actually said, "Is this a library book? Can we buy one to keep?"