I'm going to disagree with a few of the moms. I think playing a game or two is GREAT! I think games CAN be a lot of fun.
I've been to showers that played a diaper the doll game. In groups of like 5, everyone is blindfolded and then you have to diaper a doll. The winner of each "group" will challenge at the end for the winner. Unless you just want to give you a few prizes and give each of the group winners one.
The dirty diaper game is quite funny as well. Watching all the ladies sniff diapers that look bad. LOL. If you have good sports coming, this can be a blast.
If you want sit down games you could do a word scramble. Or What do you call a baby? You pick 15 to 20 different animals and then the ladies have to write down what their baby is called. Ex: COW (they would write calf next to it.) Whoever gets the most right wins.
Or if you just wanted to do one big game where you would give away 8 to 10 (or more) prizes at once and be done is the DICE GAME! Very fun. You put all the prizes in the middle and have 2 or 3 pie plates with 2 dice in each one. Set the timer for 5 minutes (or whatever) and let them go. If they shake a pair, they get a prize out of the middle. When all the prizes are gone, they can steal a prize from another person when they shake a double. When times up, everyone can open their prizes and it's over.
I highly suggest letting everyone eat while the mom is opening presents. It gets VERY LONG if you give 30 minutes to eat, then play games and THEN finally open the presents. I know the mom either has to eat BEFORE or AFTER the presents but it's much nicer for all the guests if you can combine eating and present opening at the same time. Just have the tables or chairs set up so everyone can see the mom opening the gifts.