We almost could have included Seinfeld in this thread.
It had a limited four episode run in the winter of 1990, after its pilot aired as a one shot in the summer of 1989 and finished an OK second place in its timeslot. It tested horribly with focus groups, and drew mediocre numbers for the limited Summer 1990 run. But unlike other short summer season tryouts, Brandon Tartikoff, who ran NBC programming at the time, saw something in it that no one else at 30 Rockefeller Plaza did. So he opted to give Jerry, George, Elaine and Kramer one last chance with a 13 episode run as a midseason replacement at the beginning of 1991. It almost died again on restart. Its relaunch got postponed because the initial airdate just happened to be the night the Gulf War started in January of 1991, an event that blew up every network's prime time schedule that evening.
But it started to build slowly in that 13 week run in the spring season of 1991 (when viewers like me discovered it), drew enough viewers to get another 13 week order for the fall of '91, started really gathering a following that fall and winter, got a full season production order--and by the spring of 1992, was the genuine hit we all remember. But if a few people at NBC hadn't believed in it more than they believed in some other shows with equally weak initial performance, it never would have become master of its domain...