There's no denying that this is a great way to check out new music for free/cheap, and I honestly think this will become a more common method of music distribution sometime in the future. It certainly allows easier (and legal) access to music for those who are low on cash. So share any bands who offer their albums online for free or on a pay-what-you-want basis. Hell, sometimes they are two in the same.
The only band I know of of-hand that does this is Wheatus. All of their albums (with the exception of the self-titled) are available on their site for whatever you want to pay for them, even $0. Of course, there are bonuses for donating certain amounts.
Past releases can be downloaded here.
Their newest release can be accessed right from the home page.
Anyway, they are the only band I can think of at the moment, so share any bands you know that also work on this method!