RNA is a less stable molecule than DNA, so it is subject to more mutations. Riboviruses like influenza use RNA exclusively, and as a result they mutate faster than any other kind of virus.
Virus mutation rates are measured as the mutations per genome per replication (μg) — that is, the average number of mutations that will occur each time a single virus particle (virion) copies its genome. DNA viruses — those that use only DNA at all stages of their replication cycle — have the lowest mutation rate, μg = 0.0034. Retroviruses, which use both DNA and RNA in their replication cycle, have a much higher rate of about 0.2.
Influenza and other riboviruses have an incredible μg of about 0.67 to 0.76. Since each complete virus replication cycle requires two transcriptions, that means each daughter virus has an average of 1.34 to 1.52 mutations! The superfast mutation rate of influenza is what fuels its ability to evolve and adapt, overcoming the immune system's method of recognizing old pathogens.