I have a lot of trees in my yard...and squirrels. I'm not 100% sure the squirrels are the critters doing the damage, but it seems the most likely. My neighbor says he's seen a possum in his yard before...and I'm not ruling out rats or mice.
Anyway, this is the third time this has happened. I hate to start killing squirrels to prevent it; it's kind of fun looking at them scamper up and down my trees. Plus, they might not be the offender anyway.
Here's what the damage looks like: