Originally posted by Seaside:

Actually Wolves (and probably Boars) don't die when falling overboard. They swim slightly slower than speed 1 so if you stay at that speed and stop from time to time to keep the animal in sight, it will just follow you right to your destination. Had to do this many times.

Tame boars don't follow. Wild boars do but only to attack.

I once found a 2 star boar that was not spawned at a boar stone. It was on the exact opposite side of the huge island my base was on. It took 2 1/2 in game days for me to lead it back to my base and get it in the barn to tame.