Charge conservation was an important part of the development of relativistic quantum mechanics.  This development naturally lead to the proposal of and belief in baryon conservation.

Experimental verification of a very long lifetime for the proton lead to a firm belief in baryon number conservation. Sakharov, wanting to explain the baryon asymmetry of the universe, instigated people thinking about proton decay when he threw away baryon conservation showing that a baryon symmetric universe could lead to a baryon asymmetric universe. However, his model was bold in that it proposed that the proton decayed. We now know that generating the baryon asymmetry does not necessitate proton decay. However, his proposal opened the door for the current motivations for proton decay, grand unified theories. By unifying all three gauge forces into one, grand unified theories make leptons and quarks indistinguishable at high energies. This leads to operators which violate baryon and lepton number destabilizing the proton. Interestingly, the lifetime of the proton predicted for many supersymmetric grand unified theories is in reach of upcoming experiments such as Hyper-Kamiokande. Future detection of proton decay would have far reaching implications for supersymmetric models, including the nature of dark matter. If detected, proton decay would significantly change our understanding of the laws of nature.