There are many team games available that are trust games, team building games, or teaching how to work together to solve problem games.
I would just like to mention that teams should be encouraged to be light hearted throughout the day especially when things are going right during work hours. In other words the more fun that goes on during the day the better as long as the line has been drawn to get the work done. This isn’t about goofing off but instead smiling and laughing together because so much time is spent with one another. The work place should be conducted with customers in mind with teams addressing customers in a very upbeat manner. Being able to kid around with each other assists with this.
Even having an ongoing trivia contest can be a small game that just is different from the everyday work load but does not interfer. Put a trivia question up every couple days and give eberyone who gets it right a point. Then people get interested to see if they can get points, just for fun.