Some of these games aren't particularly gymnastics related, but I know from experience are fun, especially at 2AM

.
One is hide and go seek in the dark. There are a few versions of this but when I played it we would have the person who's it sit on a mat in the middle of the floor (more or less the middle of my gym) with a big flashlight. That person would close their eyes while everyone else hid, then we'd turn off
all of the lights and the person on the mat would open her eyes and turn on the flashlight. Everyone who was hiding had to have some body part sticking out and the person on the mat would shine her flashlight around to try to see people. If someone was caught they were out, but if someone made it to the mat without being seen they were one of the winners.
Another game is capture the flag. We would divide the gym in half and each team would hide their "flag" (doesn't have to be a real flag) on their side, and then try to defend it from the other team.
There's also the ever popular seat-drop wars. I know some coaches feel that this is very dangerous, but there are some safety precausions that make it safer: have the lighter gymnast be on the side with the pit (where available), and have a rule that if you cross the centre line you're out.
Another fun game on trampoline is stick. There are different versions of it and different skills can be used depending on the age and level of the gymnasts.
I hope these sugestions help.