Boy, it's been so long since I've been to a baby shower and if I had the choice I would attend a shower that was filled with friendly chit chat and no games.
I'm not one for game playing because time is so precious and everyone is so very busy that it often takes up unnecessary time. Simplicity is best in my book right now.
If it is 'prizes' you want to give out place centerpieces on the table, tape numbers under each plate at the table or under their chairs and draw numbers for each table regarding the centerpiece.
If it is a must for games the ones I was used to were the following:
Unscramble a set of words that relate to baby items i.e. diaper stroller bottle etc
make words that relate to baby items from the mother or baby's name: i.e. Grace: Gerber, cradle etc
Ask for the person who's birthday is closest to the baby's due date
See who can remember the items on a tray and write them down after looking at it for 30 seconds before removing. Tray items: diaper pin, night light, bib, etc
Good luck and hope everyone has a fun time. :)