We present near-infrared photometry and optical spectroscopy of very low mass stars and brown dwarf candidates in the Pleiades open cluster. The membership status of these objects is assessed using color-magnitude diagrams, lithium and spectral types. Eight objects out of 45 appear to be nonmembers. A search for companions among 34 very low mass Pleiades members (M<=0.09 Msolar) in high spatial resolution images obtained with the Hubble Space Telescope (HST) and the adaptive optics system of the Canada-France-Hawaii telescope produced no resolved binaries with separations larger than 0.2" (a~27 AU P~444 yr). Nevertheless, we find evidence for a binary sequence in the color-magnitude diagrams, in agreement with the results of Steele & Jameson for higher mass stars. We apply the lithium test to two objects: CFHT-Pl-16, which lies in the cluster binary sequence but is unresolved in images obtained with the Hubble Space Telescope; and CFHT-Pl-18, which is binary with 0.33" separation. The first object passes the test, but the second object does not. We conclude that CFHT-Pl-16 is an Pleiades brown dwarf binary with separation less than 11 AU and that CFHT-Pl-18 is a foreground system. We compare the multiplicity statistics of the Pleiades very low mass stars and brown dwarfs with that of G- and K-type main-sequence stars in the solar neighborhood. We find that there is some evidence for a deficiency of wide binary systems (separation >27 AU) among the Pleiades very low mass members. We briefly discuss how this result can fit with current scenarios of brown dwarf formation. We correct the Pleiades substellar mass function for the contamination of cluster nonmembers found in this work. We find a contamination level of 33% among the brown dwarf candidates identified by Bouvier et al. Assuming a power-law IMF across the substellar boundary, we find a slope dN/dM~M-0.53, implying that the number of objects per mass bin is still rising but the contribution to the total mass of the cluster is declining in the brown dwarf regime. Based in part on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with proposal ID 7952.