As recently as six years ago it was generally agreed that all Wolf-Rayet (WR) stars were the product of mass loss induced by Roche lobe over-flow (RLOF), and that thus they were all members of binary systems. In particular, the presence of absorption lines in the spectrum of a WR star was taken as a definitive indicator that the star was a binary, as it was well known that emission alone (other than the absorption present in P Cygni profiles) was a WR characteristic. However, Niemela (1973) showed that in the WN 7 binary HD 92740 that the absorption and emission lines move in phase, proving that in at least one case the absorption spectrum originates in the WR star itself. Conti (1976) has meanwhile suggested that WR stars could form by mass loss due to a stellar wind rather than RLOF. Obviously it is well worth examining the belief that all (or even most) WR stars are binaries. The currently popular feeling is that the late WN stars (WN 7, 8, and 9) are the only possible exceptions to the traditional picture, while the members of the other subclasses are all hydrogen-poor and probably members of binaries. I hope to convince you today that this is not the complete story.