Officially, the mugs are only good at the resort at which they were purchased. Here's two possible solutions:
1) Many people have purchased mugs at Resort A, and then moved to Resort B and asked Resort B to swap their "A" mugs for "B" mugs. The resorts seem willing to do this.
2) Mugs? Who needs mugs!!! In practice when it comes to free standing soft drink islands at the resorts, WDW has a "Free Soft Drinks For ALL Guests" program. You need not bother even buying mugs. Old mugs from previous visits, mugs from other resorts, McDonald's cups, "Big Gulp" mugs, baby bottles, empty bread wrappers (as witnessed by our own DMRick), or anything else that'll hold liquid can be used to get unlimited drinks during your Disney resort stay with almost no chance of interference from CMs. So why waste those hard earned Disney vacation dollars... just take that ice bucket from your room and run down to the food court for some free Coke for your family!!!