"Just going to add - Don't kill the beavers and either take all the wood or dump it so more dams spawn."
Killing beavers, or building near their spawns (even on the shores/land) will prevent beaver dams from spawning there. If you loot a dam, please make sure there are NO items remaining, and the dam is collapsed -- this will allow a new dam to spawn soon. If you don't need the extra stuff, just hover over the item icon and press "O" to immediately drop it.
Where to Find Beaver Dams on The Island (Map)
Where to Find Beaver Dams on The Center (Map)
Written by Octopus.