My Bible study has a white elephant gift exchange every year. Each year, the leader always makes it clear that the gifts are supposed to be the tackiest, ugliest, most ridiculous thing you can find around the house, and wrap it so that it's impossible to tell what it is. No one is supposed to bring anything nice or new. This party is always eagerly awaited and is well attended. Our party was last Sunday, and Mr. Sirius and I brought two canvas grocery bags full of "stuff" from my desk, plus a couple of items that we'd bought throughout the year. You know the type of thing: you see them in the store, you buy them, you take them home, then wonder what possessed you to buy it, and it's too cheap to take back to the store. In exchange I got someone's Valentine's gift teddy bear; the bear is white and the soles of its feet are red hearts, and it has an attached heart-shaped gift box with squashed flowers on top. Mr. Sirius got two inflatable guitars that were packed in a container that had held Belgian chocolates. Other gifts were wind-up sushi toys and a head massager that looked like some kind of alien being with wire legs and an ugly wizard's head on top.
I think the people who bring nice, new things to a white elephant gift exchange are missing the point. This is supposed to be a fun exchange of tacky gifts and junk, not a contest to see who can bring the nicest present. If it's supposed to be nice gifts, then make it a regular gift exchange.