Following the recent classification of the X-ray detected object V410 x-ray 3 with a young brown dwarf candidate (Briceño et al. 1998) and the identification of an X-ray source in Chamaeleon as young bona-fide brown dwarf (Neuhäuser & Comerón 1998), we investigate all ROSAT All-Sky Survey and archived ROSAT PSPC and HRI pointed observations with bona-fide or candidate brown dwarfs in the field of view with exposure times ranging from 0.13 to 221 ks, including dedicated 64 ks and 42 ks deep ROSAT HRI pointed observations on the low-mass star BRI 0021-0214 and the brown dwarf Calar 3, respectively. Out of 26 bona-fide brown dwarfs, one is newly detected in X-rays, namely rho Oph GY 202. Also, four out of 57 brown dwarf candidates studied here are detected in X-rays, namely the young Taurus brown dwarf candidates MHO-4, MHO-5, V410 Anon 13, and V410 x-ray 3. The M9.5-type star BRI 0021-0214 is not detected. In the appendix, we also present catalogued, but as yet unnoticed B- and R-band data for some of the objects studied here.