We have measured the production of charged nuclear fragments in collisions of 1.05 GeVI A and 2.1 GeV I A proton, deuteron, alpha and carbon projectiles as well as 0.4 GeV I A alpha particles on targets of C. Cu. Pb. and H (from a CH2-C subtraction), using a double focusing spectrometer. We present single particle inclusive cross sections for the production of Z=l and Z=2 fragments in the region 0.5 ~ (p1Z)1® ~ 8.7 GVIc and oo ~ '19-1® ~ 12°. We discuss the relevance of the concept of limiting fragmentation to our data and point out possible uses of the data to study nuClear structure and particle production mechanisms. A detailed comparison is made with Glauber type models and hard-scattering models as well as the coalescence model. This work was supported by the Director, Office of Energy Research, Division of Nuclear Physics of the Office of High Energy and Nuclear Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098.