Squirrel

Squirrels skitter around forest ground and change direction constantly, so a net swing that would land on a bunny often whiffs. Shaking a forest or pearlwood tree can drop one at your feet, which is the reliable route if you are not finding any. Anything at all can kill them, and wandering enemies often will before you get there.

A netted squirrel rides in your inventory and can be released anywhere, which is how most people move critters back to a base. Building it into a cage locks it in, and short of running the furniture through Shimmer you are not getting the animal back out. They also cook into Grilled Squirrel, so the spares have a use.

There is a red variant with its own cage, and any spawn has a small chance of coming out as a Gold Squirrel, which is the one worth stopping for. A statue will produce squirrels forever, but statue critters cannot be netted and burst into smoke if you try, so statue farming is useless for gold hunting. Deeply negative luck flips them hostile, the only situation where a squirrel is a threat.