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Recently, I had a company sponsor a Facebook campaign experiment. All I offered them was a few tweets, and a banner at the bottom of the article. I've also had contest sponsored with the same offerings, but I don't think it comes down to what you offer them; Rather, I think its more about your reputation and how you run the contest. Obviously, you have a higher chance of getting your contest sponsored if you offer something in return but if you're community/site is crap...then they aren't going to give you the money/things you need anyway.
I would suggest getting companies that have a product that would tie in with your product (which is your website) and then look for companies that are just starting out trying to get their name out there, they would be more likely to say yes. In return they usually just want a small amount of advertising.