We present the results of eleven years of observations of T CrB obtained with the International Ultraviolet Explorer (IUE). The IUE spectra show a rather complex structure in which emission lines and shell-like absorption features are superposed on a relatively hot and variable continuum. The reddening-corrected energy distribution can be represented by a single power-law spectrum F(lambda) is-proportional-to lambda(alpha), with an average value <alpha> = 1.26. The changes in the UV continuum show no correlation with either the orbital phase or the optical variations. The changes in the UV emission lines (which, in addition to the lines commonly observed in exnovae, e.g., N v, C IV, and He II, also include strong intercombination transitions, e.g., N IV] lambda-1486, N III] lambda-1750, Si III] lambda-1892, and C III] lambda-1908) are clearly correlated with the variations of the UV continuum, an indication that photoionization is the main energy input mechanism, as in most symbiotic stars. High-resolution spectra, although partially underexposed, show that the C IV lambda-1550 and He II lambda-1640 lines have very broad and shallow profiles with HWZI > 1300 km s-1. T CrB has been considered the prototype of non-TNR (thermonuclear runaway) recurrent novae in which the explosion is caused by the dissipation of the kinetic energy of a burst of matter accreted by a mainsequence star. However, all evidences from our IUE observations made during its quiescent state point toward a white dwarf as the hot component in the system, in particular (1) the fact that the bulk of the luminosity is emitted in the UV (average L(UV) = 40 L., peak L(UV) = 70 L.) with little or no contribution to the optical; (2) the presence of strong He II and N v emission lines, suggesting temperatures of the order of 10(5) K; and (3) the rotational broadening of the high-excitation lines. These UV indications, together with the detection of T CrB in X-rays, and the presence of flickering in the optical light curve at several epochs, find a natural explanation in terms of accretion onto a white dwarf. With this assumption, from the observed UV luminosity we derive an average accretion rate of 1.5 x 10(18) g s-1. The luminosity of the He II lambda-1640 line (7 x 10(32) ergs s-1) has been used to provide an alternative estimate of the mass accretion rate and an estimate of the EUV-soft X-ray luminosity. The results are in agreement with those based on the UV continuum and on the theoretical expectations for a white dwarf accretor. We show also that there is no contradiction between the assumption of a white dwarf and the historical records on the spectral and photometric behavior of T CrB at the time of the 1946 outburst. An interpretation of the outburst in terms of a TNR on a (massive) WD is supported by the following facts: (1) the spectral evolution during outburst has followed the same pattern generally observed in very fast novae; (2) the photometric light curve has obeyed the same relation M(upsilon) max-t3 followed by classical novae; (3) the luminosity at maximum was super-Eddington, a distinctive signature of a TNR model. The fact that the mass accretion rate during quiescence is very high and is exactly that required by the theoretical models to produce a TNR with the observed recurrence time on a massive WD supports this interpretation. The presence of the secondary maximum in the outburst light curve, a feature generally not observed in classical novae, is interpreted as the conversion into the optical of the UV radiation from the hot nova remnant, by the optically thick, low-temperature shell observed at the time of the secondary maximum. The spectral evolution after outburst also suggests a rather low mass for the ejected envelope, as expected for a TNR in a massive white dwarf. The most serious difficulty for our interpretation in favor of the presence of a white dwarf comes from the results of a radial velocity study which indicated for the hot component of the system a mass higher than the Chandrasekhar limit. We point out, however, that the uncertainties and the difficulties involved in the measurements are such that a solution compatible with the presence of a massive white dwarf is within the observational errors.