Over the decades catch & release fishing has taken a firm hold in the sport fishing community. My guess is it started with fly fishing and more specifically, trout fishing. This is just my guess and probably because that's where I was first exposed to the practice. Wherever it began isn't really as important as the fact that catch & release fishing began. It has since spread to become more of a common practice with just about every fresh and saltwater game fish.
From my side of the rod, that's great news (even better news to the many fish that are released each season). The practice has led to better fishing in many fisheries. It also eliminated the waste of storing fish in freezers until they became freezer burned only to be discarded several months later.
It's great that catch & release continues to gain popularity with anglers, but catch & release is more than just "throwing 'em back". Taking proper care of the fish in your hands is an important element in successful catch & release fishing.
Jason Puris of TheFin.com put together a good short video with Bob Popovics, Carl Safina and Brad Burns on how to release a striped bass.
Here's a link to the video: http://www.thefin.com/ViewVideo.aspx?vid=61b5d3af-0998-4728-a4b5-f82082cdae3b