I'm always about the more we can do together OUTSIDE of cheer, the closer they become. We do a lot of team building. To be competitive nationally I feel like you have to have a team that works together and cares about eachother, or it's a losing battle. Some of our favorites are pool parties, lock-ins/sleepovers at girls houses, scavenger hunts, spontaneous game day instead of practice (as in playing games), intersquad talent show or karaoke, going to the trampoline park, holiday parties (christmas, haunted house, bonfires), team dinners, bowling, and I think the most favorite for the girls is laser tag.
We do a lot of team building incorporated into cheer practice as well if you're looking for those type of ideas.
We also use community service events as team building. We try to do something every month all season long.