Aims. By pushing the magnitude limit of high proper motion surveys beyond the limit of photographic Schmidt plates, we aim to discover nearby and very fast low-luminosity objects of different classes: cool white dwarfs (CWDs), cool subdwarfs (sd), and very low-mass stars and brown dwarfs at the very faint end of the main sequence (MS). Methods. The deep multi-epoch Sloan Digital Sky Survey data in a 275 square degree area along the celestial equator (SDSS stripe 82) allow us to search for extremely faint (i > 21) objects with proper motions greater than 0.14 arcsec/yr. A reduced proper motion diagram H z /(i − z) clearly reveals three sequences (MS, sd, CWD) where our faintest candidates are representative of the still poorly known bottom of each sequence. We classify 38 newly detected objects with low-resolution optical spectroscopy using FORS1 @ ESO VLT. Together with our targets we observe six known L dwarfs in stripe 82, four (ultra)cool sd and one CWD as comparison objects. Distances and tangential velocities are estimated using known spectral type/absolute magnitude relations. Results. All 22 previously known L dwarfs (and a few of the T dwarfs) in stripe 82 have been detected in our high proper motion survey. However, 11 of the known L dwarfs have smaller proper motions (0.01 < μ < 0.14 arcsec/yr). Although stripe 82 was already one of the best investigated sky regions with respect to L and T dwarfs, we are able to classify 13 new L dwarfs. Two previously known L dwarfs have been reclassified by us. We have also found eight new M 7.5-M 9.5 dwarfs. The four new CWDs discovered by us are about 1-2 mag fainter than those previously detected in SDSS data. All new L-type, late-M and CWD objects show thick disk and halo kinematics. Since our high-velocity late-M and L dwarfs do not show indications of low metallicity in their spectra, we conclude that there may be a population of ultracool halo objects with normal metallicities. There are 13 objects, mostly with uncertain proper motions, which we initially classified as mid-M dwarfs. Among them we have found 9 with an alternative subdwarf classification (sdM7 or earlier types), whereas we have not found any new spectra resembling the known ultracool (>sdM7) subdwarfs. Some M subdwarf candidates have been classified based on spectral indices with large uncertainties. Conclusions. We failed to detect new nearby (d < 50 pc) L dwarfs, probably because the SDSS stripe 82 area was already wellinvestigated before. With our survey we have demonstrated a higher efficiency in finding Galactic halo CWDs than previous searches. The space density of halo CWDs is according to our results about 1.5-3.0 × 10 −5 pc −3 .