How do you report 2008 dividend income for a spouse who died in 2007?

It depends.

Money can't really be paid to a deceased person. It can be paid to their estate or perhaps a co-owner of the shares or a named beneficiary.

If the dividends were paid into the estate of the deceased spouse, then the estate should have its own Tax ID number and the income should be reported on the estate's tax return. The payer should be notified of the estate's tax id number and should be asked to reissue the 1099-DIV with the estate's tax id number.

If the dividends were paid to someone else, for example a co-owner or beneficiary, the co-owner or beneficiary that received the dividends should report them on their own tax return.

If a 1099-DIV was issued with the deceased person's SSN, the real technical answer is that the payer should be asked to reissue the 1099-DIV with the correct tax ID number (either that of the estate or that of the person who was entitled to receive the dividends). In practice, it can be difficult to get this done and this situation is handled more informally. If the amounts are large, the person handling the dividends should issue a new 1099-DIV naming the deceased as the payer and the person (or estate) that received the dividends as the payee. If the amounts are small, everybody who received the money just reports it on their own tax returns. A "large" amount would be one that would require the deceased person to file a tax return if they were still alive.