We present the results of a multiwavelength survey of H I-excess galaxies, an intriguing population with large H I reservoirs associated with little current star formation. These galaxies have stellar masses M > 10 10 M , and were identified as outliers in the gas fraction vs. NUV−r color and stellar mass surface density scaling relations based on the GALEX Arecibo SDSS Survey (GASS). We obtained H I interferometry with the GMRT, Keck optical long-slit spectroscopy and deep optical imaging (where available) for four galaxies. Our analysis reveals multiple possible reasons for the H I excess in these systems. One galaxy, AGC 10111, shows an H I disk that is counter-rotating with respect to the stellar bulge, a clear indication of external origin of the gas. Another galaxy appears to host a Malin 1-type disk, where a large specific angular momentum has to be invoked to explain the extreme M HI /M ratio of 166%. The other two galaxies have early-type morphology with very high gas fractions. The lack of merger signatures (unsettled gas, stellar shells and streams) in these systems suggests that these gas-rich disks have been built several Gyr-s ago, but it remains unclear how the gas reservoirs were assembled. Numerical simulations of large cosmological volumes are needed to gain insight into the formation of these rare and interesting systems.