You can test party-goers' thinking speed and acuity with a scramble game using the names of baby-related items.
To set up scramble words, before the shower, make a list of 15 or 20 different terms, such as blanket, pacifier, bassinet, diaper and stroller. Then scramble the letters of each word, for example, writing tlarte for rattle.
At the shower, either give each guest a piece of paper with the scrambled words on it or post the words on a wall or chalkboard where everyone can view them.
Set a timer for, say, five minutes. Whoever solves the most scrambled words in that time wins!