The key word, to answer your question, is
wavelength, as in: which wavelengths are you interested in?
So far, GRBs have been seen in all wavebands, from TeV down to radio frequencies (of course, not all GRBs have been observed at all frequencies). The waveband in which GRBs release most of their energy is, unsurprisingly, that of $\gamma$ rays, with hard $X$ coming a close second at $5\%$ of the total energy release. The other wavebands make their appearance later on, during the afterglow phase and, though energetically negligible, they provide essential clues as to the location and nature of the underlying sources.
Data at $\gamma$ and $X$ frequencies is conveniently collected in the databases of the satellites having performed the observations. The other data instead are not collected by a few, centralized scientific enterprises, but most often by collections of astronomers who may or may not share their data with interlopers and/or colleagues.
As for the main satellites:
For BATSE (the GRB experiment onboard the Compton satellite), you find their data and instructions on how to reduce them at https://heasarc.gsfc.nasa.gov/docs/cgro/batse/
For BeppoSAX, the Italian satellite responsible for establishing the comsological distribution of GRBs, you find a list of the catalogs at http://heasarc.gsfc.nasa.gov/docs/cgro/db-perl/W3Browse/w3table.pl?MissionHelp=bepposax
For Swift, the NASA satellite which has provided the largest, newest, most complete observations of GRBs, you find their database at http://swift.gsfc.nasa.gov/archive/
Integral has also an important GRB database, available at http://www.cosmos.esa.int/web/integral/science-grb
The extremely important Fermi data are also available courtesy of NASA (God bless them, and their open policy), here, and then here and further here (they are all different catalogs, mind you, not three copies of the same thing).
Konus does not have a publicly accessible database, but they have published their results here (again courtesy of NASA, God bless them).
The Suzaku-WAM data are available here.
Alternatively, you may look at the IceCube catalog: though compiled to a different aim (study the possible emission of neutrinos from GRBs), it contains much information about the prompt phase, and also some about the afterglow phase. The above catalog does not include information, however, about now-dead satellites, Compton and BeppoSAX. The whole catalog is described in this preprint. This catalog is useful aslo because it contains data from satellites (Super-Agile, Konus) which do not have a publicly available database.
All of the Web sites contain information both about reducing the data, if you feel so inclined, and about journal articles where the data have been made public already (when this is the case).
Lastly, and just for the sake of completeness, you can find a database about the GRB hosts (i.e., the galaxies they reside in) with references, here.