Precise dielectric spectra have been determined at 25 C over the exceptionally broad frequency range of 0.1 <= v/GHz <= 3000 for the imidazolium-based room-temperature ionic liquids (RTILs) [bmim][BF4], [bmim][PF6], [bmim][DCA], and [hmim][BF4]. The spectra are dominated by a low-frequency process at similar to 1 GHz with a broad relaxation time distribution of the Cole-Davidson or Cole-Cole type, which is thought to correspond to the rotational diffusion of the dipolar cations. In addition, these RTILs possess two Debye relaxations at similar to 5 GHz and similar to 0.6 THz and a damped harmonic oscillation at similar to 2.5 THz. The two higher-frequency modes are almost certainly due to cation librations, but the origin of the similar to 5 GHz mode remains obscure.