(also known as an Elephant Exchange)
The basic of this is for each person to pick up a unique and inexpensive gift to be given to an "unknown" recipient. Try to keep gifts to under $15, and be prepared to receive some very interesting gifts. Also, if we exceed 12 (RSVP limit set to 24), then please try to bring a chair or 2. Also, snacks, appetizers, and desserts are more than welcome so we can make it a mini potluck.
Description from Wikipedia (for reference, these may not be the specific rules we play by):
Gifts are typically inexpensive, humorous items or used items from home. The term white elephant refers to a gift whose maintenance costs exceed its usefulness. While the first use of this term remains an item of contention among historians, one theory suggests that Ezra Cornell brought the term into the popular lexicon through his numerous and frequent social gatherings that date back to as early as 1828.
The most popular version of the White Elephant rules allows any number of participants. However, it is recommended that the number of participants be at least six. Each participant is asked to bring a gift worth no more than a pre-agreed upon amount (sometimes nothing as explained later).
To determine the gift-choice play order, participants may draw numbers from a hat. Starting with one and up to the total number of participants, the players take turn in the corresponding succession.
Once an order has been established, each person takes his or her turn choosing a gift. The first person picks a gift, opens it, and shows it to the rest of the company. Then in turn, the participants choose to either unwrap a new gift or to "steal" a previously unwrapped gift. If a gift is "stolen", the person who had their gift taken from them gets to unwrap any unopened gift; and then, the turn passes. When all the gifts have been opened, the game is over. This variant is usually used for large groups of people (25+).
Since items can be stolen, the item in your possession is not actually yours until the game is over. However, this is often amended with a rule declaring a gift "dead" or "safe" or "frozen" after it has been stolen a certain number of times (usually three). This helps the process go more smoothly and avoids, for example, a scenario of the same gift being stolen by every successive participant, and it limits the disadvantage of being among the first to choose gifts.
A variation of the game that involves more stealing of gifts (and also involves potentially more confusion) goes like this: The first participant unwraps a gift from the pile and then shows it to everyone. The next player can either "steal" an already opened gift or be adventurous and go for a wrapped gift from the pile. If the participant chooses to steal an unwrapped gift, the person whose gift was stolen now repeats their turn and either steals another person's gift (they cannot immediately steal back the gift that was just stolen) or unwraps a new gift. This cycle of stealing can sometimes continue for a long time until a new gift is chosen at which point the turn is passed to the next participant.
Another variation is to leave all the gifts wrapped until the end. Stealing is still allowed (up to a pre-defined number of times) but must be done while the gifts are still wrapped. In this case, there is no stealing after the wrapping comes off.
Variations exist even in the process of choosing the play order. For example instead of numbers from a hat, two decks of cards may be used to determine the picking order. Each deck is shuffled individually, and one of them is dealt to the players. One person flips the top card of the remaining deck, whoever has the first matching card then takes a gift. The cards are flipped again until another match is found, and that person is next to take a gift or takes someone else's unwrapped gift. This continues until everyone has had his or her turn.
Yet another variant extends the game further with a kind of sudden death situation. After the last person's turn, the first person has the option of keeping their current gift in which case the game ends or to swap with anyone else. If they choose to swap, the next person now has the option of either keeping the gift or swapping. Again at this stage, the game ends either when someone keeps a gift or when a gift has exceeded its trading limit.
One variation states that the gifts must not be purchased; but rather, the items must be things found lying around the house or the garage - things that are valuable (not garbage) but for which you have found no use.
Another option is to keep the gifts anonymous. In this case, standard-sized boxes may be used, or gifts may at least be wrapped inside-out (the white portion of wrapping paper showing) in order to help maintain the anonymity.
Using email or other social sites (i.e.: Facebook), this game may even be played online using comment streams, linked images, videos, and banter into a web-based, online party. The online variant may be tied to online gift shopping.