A search has been made for 21cm HI line emission in a total of 350 unique galaxies from two samples whose optical properties indicate they may be massive. The first consists of 241 low surface brightness (LSB) galaxies of morphological type Sb and later selected from the HyperLeda database and the second consists of 119 LSB galaxies from the UGC with morphological types Sd-m and later. Of the 350 unique galaxies, 239 were observed at the Nancay Radio Telescope, 161 at the Green Bank Telescope, and 66 at the Arecibo telescope. A total of 295 (84.3%) were detected, of which 253 (72.3%) appear to be uncontaminated by any other galaxies within the telescope beam. Finally, of the total detected, uncontaminated galaxies, at least 31 appear to be massive LSB galaxies, with a total HI mass >~1010M{sun}, for H0=70/km/Mpc. If we expand the definition to also include galaxies with significant total (rather than just gas) mass, i.e., those with an inclination-corrected H i line width W50,cor>500km/s, this brings the total number of massive LSB galaxies to 41. There are no obvious trends between the various measured global galaxy properties, particularly between mean surface brightness and galaxy mass.