One game we used to use was identifying baby related items in an advertisement from a magazine. Parent's Magazine should have lots of ads to cut out & number, making a master list of what item is which number. Some items could be Pampers disposables, Curity cloth diapers, Healthtex clothing, Carter clothing, Johnson & Johnson bath items, etc.
Another is rather silly but fun. You take 2 very large bowls; in 1 you pile in lots of cotton balls. Hand 1 person a large spoon such as a serving spoon, blindfold her/him & have them scoop the cotton balls into the empty bowl keeping their free hand behind their back.
Another fun one is making a huge long list of what a woman might have in her purse. Scissors, staples, lipstick, keys, thumb tacks, a utility bill & the list can go on & on.
This one will tax memories. Have a tray full of assorted baby stuff--bottle, pacifier, tee shirt, rattle, jar of baby food, etc. This tray can be sitting where everyone will see it & exclaim over what's on it. Later, when the hostess decides, put the tray away; hand everyone a piece of paper & pencil. Ask them to write down the items that were on the tray.
All the ideas so far are great; too bad my babyshower invites are long over. Have a good time!!!
Oh, one more idea. Not sure if anyone mentioned it. Pass around a ball of string & ask everyone to pull of a length they think measures the Mom-to-be's waistline.