We have used the Nancay Radio Telescope to obtain new global HI data for 16 giant low surface brightness (LSB) galaxies. Our targets have optical luminosities and disk scale lengths at the high end for spiral galaxies (L_B_~10^10^L_{sun}_ and h_r_>6kpc for H_0_=75km/s/Mpc), but they have diffuse stellar disks, with mean disk surface brightnesses >1 magnitude fainter than normal giant spirals. Thirteen of the galaxies previously had been detected in HI by other workers, but the published HI observations were either confused, resolved by the telescope beam, of low signal-to-noise, or showed significant discrepancies between different authors. For the other 3 galaxies, no HI data were previously available. Several of the galaxies were resolved by the Nancay 3.6' E-W beam, so global parameters were derived from multiple-point mapping observations. Typical HI masses for our sample are >10^10^M_{sun}_, with M_HI_/L_B_=0.3-1.7 (in solar units). All of the observed galaxies have published optical surface photometry, and we have compiled key optical measurements for these objects from the literature. We frequently find significant variations among physical parameters of giant LSB galaxies reported by various workers.