Many corals spread by dropping polyps like any sort of mushrooms, many leathers, Xenia, Anthelia, star polyps (aka GSP) can also do this. This is a real pain because they will start growing all over the place. Poccilopora will spread by sexual reproduction (the only SPS I know that readily does this), and can be a real pain popping up all over the place.
Also, some (para)Zoanthids:
Yellow Polyps:
Green or Brown Button Polyps:
