I was thinking of Babylon 5 too - which had a 6 season story arc, but much of what was in season 6 ended up in 5 when the network threatened to end it at the end of 5 - then they cut the Crusader (the follow-on) after 6 episodes, much to the disappointment of the fans. B5 was one of the first series (if not the first) to have an overarching story arc, which Star Trek took on board with Deep Space Nine (before that series were often much more episodic.
I've never watched Babylon 5. You've tweaked my interest now Jenny and Adam. I can think of other non sci-fi shows that have had story arcs through an entire season, even though the individual episodes are stand-alone. These are often to do with something in the main protagonist's background (e.g. The Mentalist trying to track down his wife's killer Red John; Phrynne Fisher trying to find out what happened to her missing sister when they were children). Will have to keep an eye out now for those plot points in other shows.