One great game for your baby's first birthday party is a picture matching game. Create a poster with pictures of your baby for each month of age. Number the pictures in random order as you paste them on a poster board. Next create a form for the party guests to match the baby's age with the picture number. The guest with the most correct answers wins. You can award the winner a prize.
Below is the poster that I made for my son's first birthday party. I had each guest fill out the forms on the table and put their completed form in the pot next to the forms. My guests loved the game. It also only cost me $5.00 for the poster, paper, and photos.