Just to consolidate info for you, like others have said, you need an active displayport adapter for DVI. It needs to be powered by an external source, which I believe is always a USB plug. Here is an example:
Now, here's the problem. It seems at this point these adapters are fickle at best, so while you're spending ~$100, sometimes they don't work quite right. The Sapphire adapter I ordered from newegg was defective. Sometimes problems can be solved with a flash bios of your GPU, sometimes not.
If you don't need the digital signal, I would recommend the DP>VGA adapter. I got mine at monoprice:
http://www.monoprice.com/products/product.asp?c_id=104&cp_id=10428&cs_id=1042801&p_id=5135&seq=1&format=2
It's cheaper, and according to what I've observed, it seems to work for more people than the DVI. It took some work, but I was able to get it working relatively easy (at least compared to the time I spent with my DVI adapter). Also, people seem to report more flickering issues with the DVI adapter. With native DP monitors it seems to rarely happen (although it does occasionally), the VGA adapter seems to flicker for me every few hours. If I am using the computer all day, I might get flickers 4 times throughout the day. The DVI one is reported to do it about every 15 minutes or so? Depend on who you speak to.