You can add worms to your list as well!
Also sharks can replace their teeth. Spiders can replace their legs, and creatures like sponges or sea cucumbers are pretty much cut from some where and now you have two of them types.
Worms... sort of regenerate. However, the idea that cutting a worm in half will result in two worms is a myth. Worms do end-only regeneration, meaning they regrow only from the side that has brain or similar. A vertical cut with kill a worm, and a horizontal cut results in one severed corpse, and one regenerating worm, never two worms.
In fact, many of the creatures here are end-only regeneration, regrowing arms or legs or tails. Not true regeneration.
On the other hand, flatworms are freaking awesome. You can do stuff like cut in multiple pieces, and it still regenerates.
Biologists are keen to understand how a type of flatworm known as a planarian uses powerful stem cells to regenerate an entire body from a headless sliver of itself.
www.npr.org
This is due to a fairly simple body, and large numbers of a certain type of stem cells.