Along the beach here often you find what's in my hand above.
That's a dead, stiff "skeleton" of a sea fan of the genus GORGONIA, possibly G. ventalina. Around 50 species are listed so it might be another species. You can see a living Gorgonia ventalina here.
Are Sea fans, or gorgonians, plants or animals? Well, they're known as "soft corals" and you probably know that corals are animals.
Moreover, coral masses consist of communities of many animals, and it's the same deal with sea fans. Sea fan "skeletons" are structures on which live multitudes of individual tiny animal "polyps." Each gorgonian polyp bears eight tentacles, making it look like a tiny octopus with its legs waving in the water. The tentacles catch plankton and particulate matter as the polyps filter feed. You can read much more about sea- fan anatomy and ecology, and see polyps extending their tentacles into the water, at http://en.wikipedia.org/wiki/Sea_fan.