I've heard of people setting up personal homepages where they ask
people to donate money to them for any variety of reasons...  And I
remember a news story where one college student managed to collect
enough in PayPal donations from his website to pay of thousands of
dollars in credit card debt.

My questions is whether a person doing this has to pay tax on the
income generated from such a venture.  How do IRS regulations relate
to acceptance of many small cash donations to a single person (from,
conceivably, thousands of people)?

This is no answer, but gifts are subject to tax paid by the donor
under IRS rules, though I could suspect that the IRS might want to try
to argue that someone who was that successful was in business and
earning the money, i.e., subject to tax on his "income."

My understanding of the IRS gift tax is that it is paid by the giver
of the gift, not the recipient, and doesn't kick in until $10,000. I
believe that number has or will go up, too.

Each individual can give any other individual $11,000 every year
exempt from tax on both sides. Any amount over $11,000 must be
reported to the IRS on form 709. No tax is paid until the amount over
the exemption reaches $1Million.