Wow, I AM surprised to see Frisbee Golf top Bozon's list, but in a good way. I really enjoy frisbee golf and ultimate, and I've been wondering for a long time why they can't make a game around either of them.
Ian, Frisbee Golf is like normal golf in lots of ways. You start somewhere far away from your goal (a metal "cage"-type apparatus with a bin you try to throw into), then have to navigate using your 3 or more discs (drivers, mid-range discs, putters, etc.) to the goal in the least amount of throws. There are all sorts of discs besides just the driver/putter/etc... some curve right, some left, some fly straighter – it's all about getting where you need to get in the most efficient way. The course I know best (in Lincoln, NE) has everything from long, meandering fairways, to hilly/steep terrain, and even some unique obstacles like foresty areas and creeks to cross to spice things up. It's really fun, and a great excuse to go walking around a grassy, foresty park for a couple hours on a hot summer day.
Conclusion: Frisbee Golf game for Wii featuring Ultimate and online competition =
(the only thing I would worry about would be "throwing" too hard with the Wiimote, and accidentally flinging the controller at the TV)
EDIT: Oops, like 4 other people already explained frisbee golf