When people are going to baby showers, they are expecting baby shower punch. It's a tradition that's as old as baby showers itself. Some people serve pink punch at baby girl showers; some serve blue punch for boy showers, and others serve whatever tastes good. The sky is truly the limit on what you can serve. There are so many ideas and even more variations to choose from. Traditionally, beverages served at a baby shower are non-alcoholic because the mom-to-be cannot drink alcohol. While mom-to-be still cannot drink alcohol, traditions about drinking alcohol at a baby shower have changed a bit.