Thanks. All of the responses on stopovers have opened my eyes to some interesting techniques. The <24hr transfer idea is really fascinating. It had never occurred to me that you could arrange 23-hour stops in three or four different cities on an international itinerary and have them treated as simple transfers!
I called UAL about an upcoming award flight, and I was able to arrange a 6-day stopover in DEN with no problems at all. Seems like a great option -- at least if you have friends/family in major hubs..
Anyway, thanks FT! A month ago, I wasn't even sure what a stopover *was*