XMM-Newton archival data for the Small Magellanic Cloud have been examined for the presence of previously undetected X-ray pulsars. One such pulsar, with a period of 202 s, is detected. Its position is consistent with an early B star in the SMC, and we identify it as a high-mass X-ray binary (HMXB). In the course of this study we determined the pulse period of the possible AXP CXOU J010043.1-721134 to be 8.0 s, correcting an earlier report (Lamb et al.) of a 5.4 s period for this object. Pulse profiles and spectra for each of these objects are presented as well as for a recently discovered (Haberl & Pietsch) 263 s X-ray pulsar. Properties of an ensemble of 24 optically identified HMXB pulsars from the SMC are investigated. The locations of the pulsars and an additional 22 X-ray pulsars not yet identified as having high-mass companions are located predominately in the young (ages ≤3x107 yr) star-forming regions of the SMC, as expected on the basis of binary evolution models. We find no significant difference between the distribution of spin periods for the HMXB pulsars of the SMC and that of the Milky Way. For those HMXB pulsars that have Be companions we note an inverse correlation between spin period and maximum X-ray flux density. (This anticorrelation has been previously noted for all X-ray binary pulsars by Stella, White, & Rosner) The anticorrelation for the Be binaries may be a reflection of the fact that the spin periods and orbital periods of Be HMXBs are correlated. We note a similar correlation between X-ray luminosity and spin period for the Be HMXB pulsars of the Milky Way and speculate that exploitation of the correlation could serve as a distance indicator.