St. Elsewhere (NBC, 1982-88) gained a small yet loyal following. Over the course of its six-season run, the series never ranked higher an 49th place in the yearly Nielsen ratings. It also found rather strong audience in the 18-to-49 age demographic, the demographic that is known for a young and affluent audience that TV advertisers were so eager to reach. It also earned critical acclaim during its run, earning 13 Emmy Awards for its writing, acting and directing.
Not sure if St. Elsewhere was the longest-running series on the broadcast TV networks to have never made the Nielsen Top 30.