Longest running. The Andy Griffith Show may have been a spin-off, but it only ran for 8 seasons as opposed to Frasier's 11.
And as for The Simpsons, I suppose that really depends on if you even can count it as a spin off. I mean sure, they started on The Tracey Ullman Show, but that was as a set of distinctly different short cartoons that went through some changes before becoming a show in their own right.
End of the day, I guess if we don't count The Simpsons as a spin-off, then I think what I said stands. If we do, then I'll amend what I said to say Frazier is the most successful live-action spin-off.