Because store-bought wrapping paper is so boring these days. Around the house there's plenty of gift wrapping to make your presents pop if you experiment a little. Here are a few ideas:
Paper towels: This is the one that started it all. My paper towel-wrapped White Elephant gift was the most battled over at the last Holiday party. It was so intriguing. What kind of gift could be wrapped in paper towels? Paper towels are a great, but they use a lot of tape and tear easily.
Sunday Comics: This gift wrapping idea is an homage to the comic issue of McSweeny's. Comics pages are a great way to wrap a present, and they're a lot cheaper than store-bought wrapping paper featuring the same characters. But don't stop at just the comics section of the newspaper. For your beloved meathead, think about the sports section. For your brother the CEO, how about the stocks? Where does it really end?
Aluminum foil: This is probably the most controversial gift wrap idea, because it's pretty expensive and you can get foil gift wrapping in the store that looks much better. However, you probably have aluminum foil in the house, and when you're done opening presents it's easy to recycle. And if there are cookies to take home from that holiday party, well...
Tinted Plastic wrap: This is almost a non-wrap gift wrapping, because it's transparent. But if you want to wrap and wrap and wrap until that's no longer so, I won't tell you not to. It's pretty easy to work with. You don't need tape, and even if there are creases and folds in the first few layers, pulling the last couple layers tight will make them look intentionally textured.
More ideas: There are plenty of other gift wrapping materials around the house. Here are a few more: printer paper; paper grocery bags with the labels turned out; pages ripped out of magazines, bonus for using the New Yorker; pages ripped out of dubious magazines (you know what I'm talking about); a cardboard box as-is; wax paper...
Add some more gift-wrap ideas in the comments section. I'm sure I didn't think of them all.