This is the first comprehensive, consistent survey of the ultraviolet variability properties of a large sample of blazars. All of the 14 blazars with five or more observations in a single IUE camera showed significant variability. The strength of the ultraviolet variability is positively correlated with both the apparent ultraviolet luminosity and the degree of optical polarization of the source. This is the first clear indication that the ultraviolet continua of blazars are beamed. A search for rapid variability yielded nine 'events' with doubling time scales of 0.5-7 days. These rapid flux variations and correlations argue for the standard synchrotron self-Compton model, and against the accretion disk model, which would predict slower variations and the opposite sense of correlation.