Sure, why not?
The only catch is that donations you receive are considered income (i.e. you pay taxes on it) and they are not tax-deductable for the individuals donating. That doesn't make it very appealing for either party.
I am no accountant, but I'd recommend getting smart on the IRS' Gift Tax before taking any specific 'donations.' There are specific limits under which the donation is not taxable.
Here's a decent write up on the gift tax.
I'd be interested to know if there is a difference between the handling of person-to-person gifts and person-to-for-profit-organizations... anyone?
If someone gives a donation without any return, then it would seem to be more like a gift - not taxable to you. For the donor, donations to certain kinds of organizations described and established under Internal Revenue Code section 501 can be deductible as charitable gifts on Schedule A. Gifts to people and other organizations are not.