We had a form of Yankee swap at my work's Thanksgiving celebration. Ours is called the It Game, and involves the presents being laid out along a large table, which is in a square so that things are all around. People then roll dice, which are passed to one direction. When you roll doubles, you get to take a gift. After all the gifts are claimed, they are unwrapped and examined.
Then, you do the same thing- only if you roll doubles now, you get to steal a gift you want. There is also a specific number that if you roll that, you get to cry "It!" and get something passed to you which symbolizes "it"- usually a stuffed animal.
At the end, whoever still has the "It" symbol gets the prize, and everyone else gets the gifts they stole. If you really want to trade with someone, though, and they agree, that can be easily done too.