I have had some success with a noxious smelling compound called "Ropel" which is sold at our garden stores. It is a pump spray bottle that is designed to spray onto bulbs before planting to prevent the squirrels from digging them up and snacking on them (the name stands for ROdent RePEL,lant). Because you don't want this crap on your lettuce, vegetables, etc, what I've done is soak some cotton balls in it and placed them in strategic spots around the garden where the neighbors dog or cat has been digging. You need to renew the treatment every week or so, but it seems to keep the buggers away.

(BTW, don't get a noseful of the stuff yourself - it sortof burns in the back of your throat...I wear gloves and do my flower bulb or cotton ball treatments outside)