We present a 0.6-4.1 micron spectroscopic sequence of M, L, and T dwarfs. The spectra have R~2000 from 0.9 to 2.4 microns and R=2500-200 from 2.9 to 4.1 microns. These new data nearly double the number of L and T dwarfs that have reported L-band spectra. The near-infrared spectra are combined with previously published red-optical spectra to extend the wavelength coverage to ~0.6 microns. Prominent atomic and molecular absorption features are identified including neutral lines of Al, Fe, Mg, Ca, Ti, Na, and K and 19 new weak CH_4 absorption features in the H-band spectra of mid- to late-type T dwarfs. In addition, we detect for the first time the 0-0 band of the A ^4Pi - X ^4Sigma^- transition of VO at ~1.06 microns in the spectra of L dwarfs and the P and R branches of the u_3 band of CH_4 in the spectrum of a T dwarf. The equivalent widths of the refractory atomic features all decrease with increasing spectral type and are absent by a spectral type of ~L0, except for the 1.189 micron Fe I line which persists to at least ~L3. We compute the bolometric luminosities of the dwarfs in our sample with measured parallaxes and find good agreement with previously published results that use L-band photometry to account for the flux emitted from 2.5 to 3.6 microns. Finally, 2MASS J2224381-0158521 (L4.5) has an anomalously red spectrum and the strongest Delta u=+2 CO bands in our sample. This may be indicative of unusually thick condensate clouds and/or low surface gravity.
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