What are some good exercises or activities to help someone become more graceful?

Dance, any kind: Not just ballet, but partnered dance, zumba, line dancing, tap, belly dance, nia, essentially anything that has you learning to move your body to music. Maybe it's just me, but i think music makes everyone more graceful, especially if you pay attention to how the music makes you "feel" rather than how you think you "look". If you can do it safely, try shutting your eyes to be less self-conscious.