All three illnesses are spread via direct contact with infected secretions or droplets spread by a cough or sneeze. Interestingly, humans are the only known hosts for all three viruses. This means that with enough effort to vaccinate or quarantine the illnesses, theoretically they can be wiped off the face of the earth just like smallpox.
Thanks to the vaccines and herd immunity, all three illnesses are rarely seen in the United States. Annually, there are usually less than five hundred reported cases and sometimes less than a hundred reported cases of all three illnesses combined. Almost all of these illnesses can be traced back to an unimmunized international traveler who brought the virus back to the United States from a foreign country. The virus then spread to either unimmunized individuals or people for whom the immunity from the vaccination had worn off.
The largest recent epidemic for one of these diseases occurred in 2005 and 2006 among college-age students. There were over five thousand cases of mumps in several states, centered mostly on college campuses in the Midwestern United States. That epidemic has receded, and the rate of mumps in the United States has returned to its normal low rate.
However, in countries where public health is not well funded and vaccines are not commonly available to the population, all three illnesses are very common. For example, millions of cases of measles occur yearly, with hundreds of thousands of deaths. If you are considering traveling to a country with a high incidence of any one of these three illnesses, speak to your healthcare provider about ways to decrease your risk of infection.