We have obtained projected rotation velocities (vrotsini) of a sample of 19 ultracool dwarfs with spectral types in the interval M6.5-T8 using high-resolution, near-infrared spectra obtained with NIRSPEC and the Keck II telescope. Among our targets there are two young brown dwarfs, two likely field stars, and 15 likely brown dwarfs (30-72 MJup) in the solar neighborhood. Our results indicate that the T-type dwarfs are fast rotators in marked contrast to M-type stars. We have derived vrotsini velocities between <=15 and 40 km s-1 for them and have found no clear evidence for T dwarfs rotating strongly faster than L dwarfs. However, there is a hint for an increasing lower envelope on moving from mid-M to L spectral types in the vrotsini-spectral-type diagram that was previously reported in the literature; our vrotsini results extend it to even cooler types. Assuming that field brown dwarfs have a size of 0.08-0.1 Rsolar, we can place an upper limit of 12.5 hr on the equatorial rotation period of T-type brown dwarfs. In addition, we have compared our vrotsini measurements to spectroscopic rotational velocities of very young brown dwarfs of similar mass available in the literature. The comparison, although model dependent, suggests that brown dwarfs lose some angular momentum during their contraction; however, their spin-down time seems to be significantly longer than that of solar-type to early M stars.