Rabbits mostly. We didn't have many problems but we have two dogs as well so I think the scent helped keeping them away.
Gotcha. Oddly enough, I know we have rabbits in the area but I see them very rarely. Its weird. Deer are what I'm most concerned with. We dropped some descent change a few years ago on some landscaping. Woke up the next morning and every hosta they had planted was eaten down to the nub. My wife is a very calm, rational forgiving woman but man she was pissed. I've read that deer don't like marigolds so I may put some of those in planters if I do decide to build the boxes.