We present high-resolution echelle spectroscopy of 39 dwarfs with spectral types between M6.5 and L0.5. With one exception, those dwarfs were selected from the Two Micron All Sky Survey database using photometric criteria, (J-K_S) ≥ 1.1 and K_S ≤ 12.0, and therefore should provide a sample free of the kinematic biases that can affect proper-motion–selected samples. Two of the stars, 2MASSI J0253202+271333 and 2MASSW J0952219-192431, are double-lined spectroscopic binaries. We have used our observations to search for Li I 6708 Å absorption, characteristic of substellar mass; estimate the level of chromospheric activity through measurement of Hα emission fluxes; measure rotational velocities via line broadening; and determine radial velocities and Galactic space motions. Two dwarfs have strong lithium absorption, the previously known brown dwarf LP 944-20 and 2MASSI J0335020+234235, which we identify as a probable 0.06 M brown dwarf with an age of ~1 Gyr. We have investigated the prospect of using the observed frequency of lithium absorption among ultracool M dwarfs (M7 to M9.5) as a probe of the initial mass function, comparing the observed frequency against predictions based on recent theoretical models of low-mass dwarfs and an assumed star formation history. Our results show that the conclusions drawn are vulnerable both to systematic differences between the available models and to incomplete local sampling of the most recent star formation events (ages less than 10⁸ yr). The latter consideration stems from the mass-dependent rate of evolution of brown dwarfs. Even given those caveats, however, the available observations are difficult to reconcile with Salpeter-like power-law mass functions (α ≥ 2) for masses below 0.1 M. A comparison between the rotational velocities and Hα fluxes shows no evidence for significant correlation. The mean activity level of the ultracool dwarfs lies almost a factor of 10 below that of early- and mid-type M dwarfs. The relative number of dwarfs with v sin i < 20 km s^-1 with respect to greater than 20 km s^-1 is independent of spectral type. Finally, velocity dispersions derived for our photometrically selected sample of ultracool dwarfs are significantly lower than those measured for nearby M dwarfs but show remarkable similarity to results for earlier type emission-line (dMe) dwarfs. The latter are generally assigned ages of less than ~3 Gyr.