There are lots -- insects, mussels, earthworms, many amphibians, amoebae, tortoises, birds, spiders, flatworms, liver fluke, woodlice, lobsters, feather stars - as I say, lots. It's almost easier to say which ones do have teeth.
If by "animals" you meant "mammals", it's a shorter list. Many mammals have no teeth showing when born, though usually they are there, hidden beneath the gums.
Some have no teeth at all. My granny was a mammal, and she only had two. They did not meet.
Mammals which specialise in eating ants often have no teeth, or very small peg-like ones -- for example, echidna, the South American ant-eaters, pangolins, aardvark, and I think some armadillos. The baleen whales have fibrous plates instead, for filtering fish and crustaceans out of sea water. There are probably more I can't remember at the moment.