Pin trading, although you've got to buy pins to start with, but they're easy to find at deep discount.
Resort tours and activities. We love the Jiko/Boma tour at AKL and the tour of Artist Point at WL. Cultural representative activities at AKL- love the storytelling by the firepit and the use of the night vision goggles. There are things though at every resort, as a PP mentioned, check out the info you get when you check in.
During Christmastime, visit all the Santa's at each country to learn about the history and origin of those traditions, plus I love seeing all the Santa outfits.
Off Kilter esp. but also the other entertainers around World Showcase. There are so many if you stop and browse vs. just marching through to get to the next attraction.
Ping-pong and basketball- love this over at OKW.
Afternoon poolside games and dances. We also enjoyed this immensely over at OKW when the kids were younger.
All I can think of right now, but I'm sure there are more!---Kathy