Question
How do I stop groundhogs in particular, as well as cats from using my yard as their bathroom.  I assume it must be a groundhog because I saw what looked like one coming out of my neighbor's never used shed and the stools are too large for cats. It could also be a skunk since we have smelled that odor coming/going into the garage or a raccoon.

Answer
Prevent the woodchuck by fencing your yard in accordance with the directions at http://www.icwdm.org/Prevention/decks.asp  even though it is for decks, just transfer information to the fence.

As for free-ranging cats, they are an environmental scourge. Unfortunately, the cat lobby is extremely vocal and powerful so leash laws on cats are regrettably unlikely. It is one of the reasons why I laugh at the notion that Americans care about the environment. But that is another story.

Fencing will keep out cats too but you will need to look at fences such as those built by Purrfect fence to stop their climbing.
Electric fences work great too but regrettably, most towns have antiquated laws that prohibit them. Some states may allow you to employ lethal control on cats, but you need to look into that.

Further details on possible remedies at http://icwdm.org don't hold your breath on an "easy" solution though. If it sounds too easy, it won't work.  

By the way, I don't hate cats, I own two, INDOOR cats.