Consider the makeup of the group when choosing the right games for a baby shower. Some showers are held for church groups, while others feature coworkers and friends, and still others are just for relatives. The various sensibilities of the people attending dictate the choice of the game.
If the baby's future grandmother hosts the shower and invites mostly her friends, games that involve less physical activity might make the best choice. These tend to involve taste tests, drawing and writing rather than moving around the room. They also might involve card-based games, such as Memory and Baby Shower Bingo.
Showers that have younger guests, such as those hosted by a friend of the mother-to-be, can involve more physically active games. Some of these involve contests that time guests' ability to change a diaper on a doll or fashion "shows" in which teams have a "pregnant" team member who has to dress up in a maternity outfit, with toilet paper inside the clothing to simulate pregnancy. A fun "triathlon" tests how quickly guests can hang baby clothes from a line, while also talking on their cell phones and holding a baby doll.
Games at a shower for a church group should stay away from bawdy references to the "activity" that put the mother in her current condition. Games should instead focus on such things as providing advice for the mother or having a contest to sort mismatched baby socks in a set amount of time.