Just a guess, but I doubt that the monotremes (e.g. platypus, echidna) would have bellybuttons since they do not have an umbilical cord. Will have to look that up.....
Platypus are the only member of the family Ornithorhynchidae, order Monotremata, and are, as akaestie points out, mammals that lay eggs. They would not have navels but are such an unusual order of mammals that they are often overlooked in discussions of this type. At least that's my story and I'm sticking to it...
Only the Eutherians or "true mammals" have a placental development of a type that leads to the formation of umbilicus. So on top of the monotremes, marsupials don't have them either. So to answer the question as asked, no a great many mammals don't have navels, just the Eutherians.
For marsupials, such as kangaroos, wallabies and opposums, the placenta is rather egg like in that it consists of a yolk like structure. The infant remains in this state for only a very short time after fertilization (this in itself is quite an unusual process), is born into the pouch and must make its way to a nipple, where it attaches itself (to small to suck) until its strong enough to emerge...