What is the difference between "ordinary dividends" and "qualified dividends"? My Form 1099 dividend statements were marked by the companies as both.

Qualified dividends are a subset of your ordinary dividends. Qualified dividends are taxed at the same tax rate that applies to net long-term capital gains, while non-qualified dividends are taxed at ordinary income rates. It is possible that all of your ordinary dividends are also qualified dividends. If you have qualified dividends, you should use the qualified dividends and capital gain tax worksheet in the Form 1040 instructions to calculate your tax and take advantage of the lower rates on capital gains and qualified dividends.