We have compiled L and M photometry of 63 single and binary M, L,and T dwarfs obtained at UKIRT using the MKO filter set. This compilation includes new L data for 8 L dwarfs and 13 T dwarfs and new M data for 7 L dwarfs, 5 T dwarfs, and Gl 229A. We compute L_bol, BC_K, and T_eff for 42 dwarfs whose flux-calibrated JHK spectra, L photometry, and trigonometric parallaxes are available, and we estimate these quantities for 9 other dwarfs whose parallaxes and flux-calibrated spectra have been obtained. BC_K is a well-behaved function of near-IR spectral type with a dispersion of ~0.1 mag for types M6-T5; it is significantly more scattered for types T5-T9. T_eff declines steeply and monotonically for types M6-L7 and T4-T9, but is nearly constant at ~1450 K for types L7-T4 with assumed ages of ~3 Gyr. This constant T_eff is evidenced by nearly unchanging values of L-M between types L6 and T3. We compare the observed K, L, and M luminosities of L and T dwarfs in our sample with those predicted by model atmospheres with varying surface gravities and sedimentation efficiencies. The models indicate that the L3-T4.5 dwarfs generally have higher gravities (log g = 5.0-5.5) than the T6-T9 dwarfs (log g = 4.5-5.0). The predicted M luminosities of T dwarfs are 1.5-2.5 times larger than those derived empirically for the T dwarfs in our sample. This discrepancy is attributed to absorption at 4.5-4.9 um by CO, which is not expected under the condition of chemical equilibrium assumed in the models. We determine that the L3 dwarf Kelu-1 and the T0 dwarf SDSS J0423-0414 are probable binary systems. We compute log(L_bol/L_sun) = -5.73 +/- 0.05 and T_eff = 600-750 K for the T9 dwarf 2MASS J0415-0935, which supplants Gl 570D as the least luminous and coolest brown dwarf presently known.
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