We describe our studies of the radio and high-energy properties of Rotating Radio Transients (RRATs). We find that the radio pulse intensity distributions are log-normal, with power-law tails evident in two cases. For the three RRATs with coverage over a wide range of frequency, the mean spectral index is -1.7pm0.1, roughly in the range of normal pulsars. We do not observe anomalous magnetar-like spectra for any RRATs. Our 94-ks XMM-Newton observation of the high magnetic field RRAT J1819-1458 reveals a blackbody spectrum (kT ~130 eV) with an unusual absorption feature at ~1 keV. We find no evidence for X-ray bursts or other X-ray variability. We performed a correlation analysis of the X-ray photons with radio pulses detected in concurrent observations with the Green Bank, Effelsberg, and Parkes telescopes. We find no evidence for any correlations between radio pulse emission and X-ray photons, perhaps suggesting that sporadicity is not due to variations in magnetospheric particle density but to changes in beaming or coherence.