My neighborhood is infested with squirrels, which (as I've discussed before) may have a lot in common with rats, but get a pass because of the bushy tail. There's also a big groundhog that's been digging into a shed a few doors down -- that neighbor keeps trying to block off the entry, but it just digs along side of the concrete blocks to get back in. It's not very neighborly of me, but I cheer for the marment -- I like to watch it -- it's a survivor and not damaging any of my stuff. I see a pair of falcons frequently that must nest somewhere in the neighborhood; I suspect that they help control the squirrels. I've also seen possums, a raccoon, a fox, and even a coyote, which seems strange since I live in the city limits, but before the housing crash, development along the Ohio river pushed some animals got out of their habitat.
Anyway, I wouldn't even try to maintain a garden because of the squirrels, but I can certainly see your point about that rabbit.