Call it what you will-- Dirty Santa / White Elephant / Yankee Swap -- the aim of this party game is to steal your way to the best present in the room!
The general rules of the game are to form a circle with all the wrapped presents in the middle, then one person (often chosen through drawing numbers) picks a present and opens it. The next person then has the choice of either opening a present or stealing the one the first person chose. This continues around the circle, with anyone whose gift is stolen having another turn to either open a gift or steal someone else's. There are variations to help keep things fair / keep things moving in the game, such as if something has been stolen three times that it is then "frozen" or "safe", that each gift can only be stolen once per turn (to avoid a back-and-forth "war" between two players), that the first player has an additional turn at the end to allow them to steal any "unfrozen" gift, etc.
Often there is a limit on how much to spend on the gift you bring (usually somewhere between $10 - $25) and sometimes the host will request gifts follow certain themes (everyone bring an ornament, everyone bring a food or drink item, etc), but often it's whatever you want to do that doesn't go past the dollar limit. In this case, it's up to you to decide if you want your gift to be funny / silly or something actually useful that will be fought after. You can also try for both with amusing gifts that serve a genuine purpose, such as these Sweater Mug Huggers (handcrafted by artisans in Peru) from Uncommon Goods:
Or this giggle-inducing desk calendar from Awkward Family Photos:
If your aim is to be purely silly / funny, Amazon has scores of suggestions that you can find simply by doing a search for "white elephant gifts", "dirty Santa gifts", etc., and you can even specify the dollar limit (like this list of gifts for under $20).
If you want your gift to be eminently useful, consider some of the following tips:
1) You can't go wrong with a gift card. Yes, they're not the most entertaining gift at the party, but when was the last time you saw someone be sad that they have $25 to spend on Amazon or at Starbucks?
2) Go for unisex. If you bring that super-handy set of bra clips and the gift ends up with Steve, he may be a little less than thrilled.
3) Do a cash craft. Consider going the creative route and doing something made from money like this bouquet made from dollar bills, wire, and floral tape from Bridget Green on eHow Arts and Crafts (no glue or tape involved, so the bills stay useable-- see a video tutorial here).
4) One-size-fits-all is your friend. Fuzzy socks probably won't fit both the guest who came wearing a size five shoe and the one in a size twelve, but a fuzzy blanket will.
5) Bring on the booze. A nice wine or bottle of liquor is a generally safe call; even if the person can't use it themselves, it's a good candidate for re-gifting.
6) Big Money....? If they're available in your state, think about giving lottery tickets as your gift-- it provides the recipient with some excitement even after the party is over without the risk of having lost their own money (and you never know-- it could mean a big win!) If you're more into the long game, consider giving a stock gift certificate (for fractional shares of companies like Apple, Google, etc). This option would require some kind of IOU card or something until you know the recipient's name in order to officially send it, but is otherwise really simple and takes just a few minutes to do (you can send one for as low as $20 through Spark Gift).
7) Up their food game. Small kitchen appliance like a sandwich press, milk foamer, etc. are fun, useful, and often something someone wouldn't get for themselves (but will nonetheless enjoy).
8) Do a duo. It's totally legit to split your gift into a pairing of two smaller things that go hand-in-hand (like a coffee mug with a Starbucks gift card, hat and gloves, etc.)
9) Baskets make it bigger. If you're crafty, think about putting together a themed gift basket (movie night, chocoholic, etc). Throwing in multiple small items with a bunch of colorful shred or tissue paper and topping it off with a fancy bow is sure to impress (see a tutorial here from Ann's Gifts & More on how to make a basket like the one below).
10) Hit the clearance rack. Places like Target, Big Lots, Wal-Mart, etc. all have clearance sections (sometimes in each department, sometimes a series of shelves in just one area of the store) that allow you to get more bang for your buck-- if your dollar limit is $25 and you find a $40 item half off, it keeps you under budget and gives you the smug satisfaction of being a shopping diva.
When in doubt, just ask yourself if the gift you bring to your Dirty Santa Party is something you'd like to receive (or would be proud to re-gift), and you're sure to hit a home run.