There are dozens of fun office gift exchange games people can play during the Christmas season. Officemates might have a "secret Santa" gift exchange or a popular "white elephant" gift exchange. All are popular and always fun, provided the rules are clear and everyone understands them.
One of the most popular office games involving Christmas gifts is the "white elephant" gift exchange. The rules can vary depending on the office and participants, but generally it works something like this. Each person participating purchases a gift not to exceed a certain dollar amount (determined in advance and might range from $5 to $20, again depending on the group). The object here is a fun gift, so anything particularly practical is not welcome. You're looking for unusual and interesting, perhaps funny, and something other people will want.
Everyone who's participating in the exchange gets a number (the number should be the same as the number of presents). The numbers should be they drawn out of a hat or something else (perhaps a Santa hat, in recognition of the season?). So, the person who draws number "1" goes first and picks a present. They open it and keep it. The second person can either pick a different present or they can "steal" the first present. They can't open a present until they are sure they are keeping their choice and not picking the first gift. This continues until everyone has a present. Any present that's been opened can be subject to stealing, but a gift can only be stolen three times.
At the end of the game, the person who was the first to open a present can steal a gift if they choose, since they didn't have an opportunity earlier.
In this game there's always one gift that everyone wants and will steal over and over again. What makes it fun is trying to figure out who is going to get the most coveted gift. In some cases, people can end up with the gift they brought.
Originally the "white elephant" gift exchange was a way for people to "regift" or give someone a gift they themselves received and don't want. For a fun twist, you could ask people to bring something from their home like that, or you can require they purchase something (with the aforementioned limit on spending).
There are many varieties of the Secret Santa game, which is so popular in offices, but one option that's fun involves putting a dollar limit on the purchase and having participants actually make "Santa lists". Here's how it works: Those participating create a little list for "Santa". There should also be a dollar limit placed on this gift exchange, so if that is $10, then people should only list items on their Santa list that can be purchased for $10 or less.
Everyone who is participating draws a list out of a hat, or some other object, and sets about shopping for that person. They know who they are shopping for, but the recipient doesn't. On exchange day, the Secret Santas must deliver the gifts to their officemates' desks without being seen. Those participating can decide if they want people to sign the cards attached to the gifts, or if the secret should stay a secret. If they choose the latter, gift giving can be interesting, since it's anonymous, but many people choose to have cards signed so in the end, people who to thank for their gifts.