Singing songs with instrumental accompaniment sounds fun. But if you don't have an instrument, or if you don't have a songbook, a better option would be simple vowel and harmony exercises, if you can get to that magical point where everyone's listening to everyone else.

There's also a cool rhythm exercise you could do. The basic idea is to sway to the beat, actually turning your body and taking a step on the beat, and clapping to the beat as well, with your hands moving even more than your body. Once everyone's into the groove, you can start subdividing - into half of the beat, and thirds of the beat, and fourths and fifths. Then you can play follow the leader (TEH CULT INDUCTION!!). And for extra challenge you can have some people do 2 while other people do 3 (the rhythm is "george washington"), and then swap every few measures. When you do this, the people clapping "2" will get lost - one trick to help get un-lost is to go back to clapping 1 for a few beats when you recognize you've been seduced by those 3-clappers.