Captain James T. Kirk was Star Trek's first and perhaps still most famous captain - so where did his story go after The Original Series films? Kirk - played with hammy bravado by William Shatner - commanded the USS Enterprise during its five year exploratory mission in the mid-23rd century; flanked by his top confidants, Commander Spock and Dr. Leonard "Bones" McCoy, these adventures made up the three seasons of Star Trek: The Original Series, which aired from 1966 to 1969. After The Original Series was cancelled by NBC, the show became a hit in syndication, which would lead to the franchise's revival on the big screen.
The next time the The Original Series cast was seen in live-action was in 1979's Star Trek: The Motion Picture. That story picks up several years after the events of the TV series, with Kirk now an admiral who no longer commands a starship. He would, of course, find an excuse to jump back into that chair on the Enterprise's bridge, where he would stay for five more Star Trek movies, the last of which was 1991's Star Trek VI: The Undiscovered Country, which ended with the Enterprise being decommissioned and Kirk and his crew standing down. While this was the end of the story for most of the The Original Series crew, James T. Kirk would live on.
Plans had long been in place for the cast of Star Trek: The Next Generation to inherit the Star Trek film franchise after The Original Series' cast retired. The cast and crew of The Next Generation - Patrick Stewart in particular - were adamant that their first film be a transitional one, with the original Star Trek cast handing things off to the new crew. This was easier said than done, as The Next Generation was set roughly a century after The Original Series. With the exception of the long-lived Vulcan Spock, most of the The Original Series' crew should've been dead by the time of Jean-Luc Picard and Data.
To unite Picard and Kirk, Star Trek would have to turn to one of its most tried and true weapons: time travel. Set shortly after the events of The Undiscovered Country, 1994's Star Trek: Generations opens with the christening of the new USS Enterprise-B in 2293, under the command of Captain John Harriman. Kirk, Scotty, and Chekov are invited to the event as goodwill ambassadors, but the newly minted vessel quickly finds itself on an unexpected rescue mission when it receives a distress call from two El-Aurian refugee ships, which are being rocked by a strange energy ribbon. Both El-Aurian ships are destroyed, though a few refugees are transported to the Enterprise - including future Picard confidant Guinan (Whoopi Goldberg) and Tolian Soran, a seemingly demented scientist who begs to be sent back to his exploding ship. The Enterprise hull was badly damaged in the rescue, with Kirk himself apparently killed, sucked into space saving lives.
However, this still wouldn't be the end of Kirk. The energy ribbon in space turned out to be a dimensional anomaly called the Nexus, which essentially granted its residents whatever their heart desired. Soran was obsessed with returning to the Nexus, and was still attempting to access it 80 years later. This time he was successful; though he re-entered the Nexus, he destroyed an inhabited planet to do it, and sucked Jean-Luc Picard into the ribbon with him. Once there, Picard was surprised to find Kirk, having not aged a day, still milling about his own personal paradise. Picard convinces Kirk to go back in time to help him stop Soran and save millions of lives one last time.
Picard and Kirk are ultimately able to stop Soran and save the star system, but at a high price; Kirk sacrificed himself to deactivate a sun-killing missile, falling from a broken bridge to his death. His last few minutes were spent with Picard, who assured him he had made a difference once again. Many fans found his death to be unsatisfactory, essentially succumbing to a minor villain with none of his crew or his ship. It remains a bone of contention for fans to this day. Generations would be the end of James Kirk's story in the Prime universe - though he'd be reborn in the alternate universe J.J. Abrams Star Trek movies (the Kelvin timeline), played by Chris Pine instead of William Shatner. Shatner himself has admitted it's unlikely we'll see him portray the character again, so the story of Captain James T. Kirk likely ended where it began - with the man saving lives on a bridge.