We present the initial results from a survey for planetary-mass brown dwarfs in the Taurus star-forming region. We have identified brown dwarf candidates in Taurus using proper motions and photometry from several ground- and space- based facilities. Through spectroscopy of some of the more promising candidates, we have found 18 new members of Taurus. They have spectral types ranging from mid-M to early-L, and they include the four faintest known members in extinction-corrected K_s_, which should have masses as low as ~4-5 M_Jup_ according to evolutionary models. Two of the coolest new members (M9.25, M9.5) have mid-IR excesses that indicate the presence of disks. Two fainter objects with types of M9-L2 and M9-L3 also have red mid-IR colors relative to photospheres at =<L0, but since the photospheric colors are poorly defined at >L0, it is unclear whether they have excesses from disks. We also have obtained spectra of candidate members of the IC 348 and NGC 1333 clusters in Perseus that were identified by Luhman et al. Eight candidates are found to be probable members, three of which are among the faintest and least-massive known members of the clusters (~5 M_Jup_).