We present observations and interpretation of the Type IIn supernova SN 2008am discovered by the ROTSE Supernova Verification Project (RSVP). SN 2008am peaked at approximately -22.3 mag at a redshift of z = 0.2338, giving it a peak luminosity of åisebox-0.5ex 3 × 10$^44$ erg s$^-1$ and making it one of the most luminous supernovae ever observed. The total radiated energy is sime2 × 10$^51$ erg. The host galaxy appears to be an SB1 of normal luminosity (M_r’ ̃ -20) with metallicity Zi̊sebox-0.5ex 0.4 Z $_sun$. ROTSE upper limits and detections constrain the rise time to be rs̊ebox-0.5ex 34 days in the rest frame, significantly shorter than similar events, SN 2006gy and SN 2006tf. Photometric observations in the ultraviolet, optical, and infrared bands (J, H, K$_s$ ) constrain the spectral energy distribution evolution. We obtained six optical spectra of the supernova, five on the early decline from maximum light and a sixth nearly a year later plus a very late time spectrum (rae̊box-0.5ex 2 yr) of the host galaxy. The spectra show no evidence for broad supernova photospheric features in either absorption or emission at any phase. The spectra of SN 2008am show strong Balmer-line and He I łambda5876 emission with intermediate widths (raib̊ox-0.5ex 25 rA ̊in the first raisex̊-0.5ex 40 days after optical maximum. The width formally corresponds to a velocity of raiseb̊-0.5ex 1000 km s$^-1$. We examine a variety of models for the line wings and conclude that multiple scattering is most likely, implying that our spectra contain no specific information on the bulk flow velocity. We examine a variety of models for the ROTSE light curve subject to the rise time and the nature of the spectra, including radioactive decay, shocks in optically thick and optically thin circumstellar media (CSMs) and a magnetar. The most successful model is one for which the CSM is optically thick and in which diffusion of forward shock-deposited luminosity gives rise to the observed light curve. The model suggests strong mass loss and a greater contribution from the interaction of the forward shock with optically thick CSM than from the reverse shock. Diffusion of the shock-deposited energy from the forward shock is found to be important in accounting for the rising part of the light curve. Although there are differences in detail, SN 2008am appears to be closely related to other super-luminous Type IIn supernovae, SN 2006gy, SN 2006tf, and perhaps SN 2008iy, that may represent the deaths of very massive luminous-blue-variable-type progenitors and for which the luminosity is powered by the interaction of the ejecta with a dense CSM.