Fun engagement party games include bride and groom bingo, trivia questions about the couple and plant the kiss on the groom or bride, an engagement party version of pin the tail on the donkey. Specific games for engagement parties depend on the crowd and the personalities of the engaged couple. The couple may or may not want to be very involved in the games; they might enjoy just being bystanders.
Another fun game idea for an engagement party is to hold an amended version of the newlywed game, with questions meant for engaged or committed couples. Create a bunch a fun questions that are asked during the game in several different categories. The more questions, the better, so ask a friend or family member to assist with creating the questions and categories. Either beforehand or during the party, ask the engaged pair and a few other couples to participate, and have them compete against each other to see who gets the most right answers individually and as a couple.
An athletic couple might want to hold a sort of field day, with three-legged races featuring garters as connectors and other not-so-strenuous physical activities. Musical couples can enjoy several rousing rounds of karaoke. Prizes for each game include gifts aimed at a specific theme or standard fare such as candy, wine or gift cards.