I have two squirrels living on the oak tree on my lot, they planted a few hundred oak trees in my yard this year. There are oak seedlings growing everywhere.
But the big problem I had was that something was chewing off the branches of my bonsai. Both from the trees in pots and from some trees in the ground. I had a japanese beech that took three years to grow some nice balanced branching all around, and one morning it ended up looking like a literati, with no branches. First I blamed the squirrels, but then I noticed that the culprits were the roof rats (a smaller version of the large norway rat).
So right now I am waging a war against them and the squirrels look rather innocent, compared to these guys.
Just this morning, a few hours ago, I've caught two of them in my live-trap. I placed 5 of these traps, all over my yard. I started doing it a few days ago, and today I had the first two hits.
http://www.doyourownpestcontrol.com/traptemp.JPG
Once I have them in the cage, I drive up to the trailhead a few miles away from my house and release them in the wild.
By the way, this trap is also designed for squirrels, but it looks like the rats are much faster to get in. I keep the traps constantly armed and loaded, so I expect that within a few months, the rodent population will drastically decrease in my backyard.
The problem of squirrels digging in bonsai pots can be solved easily by placing a collar, made of screen, around the base of the tree. The collar looks like a disk, with a hole in the middle (where the trunk is), and the edge of the disk should extend far beyond the edge of the bonsai pot. This way the squirrel will walk on the screen, and can't dig. Usually they give up after the first few tries and find an easier place to dig.
And, incidentally, this collar is also good to block out the sun hitting the bonsai pot (which is a big problem here in So. Cal.). I use them to also protect the moss on the soil from the strong sun, and to keep the pot cool. It's easy to take them off and put them on at any time.