I woke up wondering what American prime-time scripted TV show was the most successful in history, if you include not only the number of seasons it ran but also the number of seasons its spinoffs ran.
My initial guess was Law and Order, but I figured that someone on the Internet must have done the research already.
So far, I have not found it.
Looking at the Wikipedia entry for TV spinoffs, which includes many non-American and non-prime time shows, my guess may be right, but I didn't go through the entire list. Also I am counting partial seasons as whole. To be accurate, the list should really be of the number of episodes.
Notable ones (I am including spin offs of spin offs as well, and my counts might be off):
Law and Order: 42 seasons (not including non-US spinoffs)
All in the Family: 38 seasons (lots of aborted spin-offs, not sure how long they lasted)
Love, American Style : 34 seasons (includes Happy Days)
Dallas: 27 seasons
CSI: 24 seasons
UPDATE: Jonah mentions Star Trek, for which I count 28 seasons. (He says 30, but I find it easiest to just use Wikipedia's dates for the series' beginning and end.)