1) If you entertain semi-regularly, buy a large stack or two of plastic pint glasses. A lot nicer to drink out of than Dixie cups, they’re cheap enough to not worry about a couple getting broken or stolen, and they’re substantial so most people will keep up with them a bit better since they don’t feel disposable.
2) If you have to use disposable cups, put your guests’ names on them. One per person. Chances are, people will keep up with their own, and they might just feel bad leaving cups with their name on them scattered across the area.

You could also use a hybrid of the 2 thoughts and use tape to put names on the plastic pint glasses.