One suitable game to play at an office Christmas party is an ice breaker game, such as taping a picture to each guest's back while other guests help him figure out who or what he is. Another game is to print out single lines from popular Christmas songs as guests take turns guessing the song titles for an allotted time period. The guest with the most right answers wins a special gift card.
One game idea is a twist on the hot potato game. Take one great gift or one gag gift, and wrap it in several layers of gift wrap. Each guest takes turns to remove one layer of paper at a time. The guest who unwraps the final layer wins the gift.
Another game idea is a Christmas movie titles game. Print a list of movie titles and a list of characters from those movies, in a jumbled order. The guest who gets the most correct pairings wins a special gift card.
One idea is a relay race of two or three teams of people. Each group takes several gifts and goes to the "starting line." Someone says, "Go," and the first person from the group runs to the "finish line" and places the first box on the floor. The next person repeats this, placing the second gift on top of the first. The first team to successfully stack all their gifts wins, while a stack that falls over disqualifies that group.