UPDATE: added another version using a curve path instead of bones. I recommend trying both and seeing which works best.
Made this because I was too lazy to look for a tentacle model online. It doesn't have some super fancy rig or anything, just bones (or a curve if you pick that one instead)
Quick note: the tentacle mesh has a solidify modifier on it for the sole purpose of making it thicker, don't be afraid to change it and play with it :)