Diff’rent Strokes ended in 1987, and Facts ended in 1988, so I would think they qualify.
Would it be safe to say that All In The Family had the most spinoffs?
All In the Family
Maude
The Jeffersons
Good Times
Gloria
??? Hauser Street (?)
Also
Archie Bunker’s Place
Don’t worry, most murder laws were passed before they were born, so they don’t care if we kill them!!! 
The nighttime soap opera “Knots Landing” was a spin-off of “Dallas.” It lasted about as long as the original series, so it could qualify as a “success.”
“Baywatch” spun off into the unintentionally hilarious X-Files rip-off “Baywatch Nights.”
“The Lone Gunmen” was a spinoff, albeit not a very successful one. And whenever they change the name (and most of the cast) of a kid series like “Saved by the Bell” or “Mighty Morphin’ Power Rangers,” I guess the successor series could be considered a spinoff.
Was “The Wild Thornberries” a spinoff of anything? It sure looks a lot like the “Jumanji” cartoon…
Hank Hill was NOT in the Beavis And Butt-Head movie… I know this had already been stated, but I wan’t to stress it.
No, just another Klasky/Csupo project. Which, it is going to be revealed, exists in the same universe as Rugrats as the two groups will meet.
The Rugrats is going to have a whole slew of spin-offs this season. But they haven’t been good (or at least appealed to adult me) since Dil appeared. I’m fairly certain they will mostly do very well.
704 Hauser Street
I thought it was just a continuation of All In The Family once Mike and Gloria left.
And then there would be The Colbys which was a spinoff from Dynasty.
And isn’t Bold and the Beautiful a spinoff from Young and the Restless?
Married With Children had Top Of The Heap with a very young Matt LeBlanc and Joey Lauren Adams.
The Golden Girls spawned Empty Nest and The Golden Palace.
Mary Tyler Moore left us with Rhoda, Phyllis, Lou Grant, and a Carlton the Doorman special.
Mike and Gloria left at the end of the 8th season and were in California through the 9th as Archie and Edith adopted Edith’s cousin’s daughter. It appears the name change (or new series) was an attempt to refresh the story line by bringing the show to a new place.
Reading through the entire run of “Archie Bunker’s Place” was almost as depressing as reading through the entire run of “Jeff’s Collie”/“Timmie and Lassie”, “Lassie.” Poor dog always got left behind.
“AfterMASH” from “MAS*H”
“Misadventures of Sherrif Lobo” from “BJ and the Bear”
“Delta House” from “Animal House”
“Archie Bunker’s Place” was All In the Family after Jean Stapleton left and the Edith character was killed off.
Melrose Place and The Heights were introduced via characters appearing on Beverly Hills, 90210, but I don’t necessarily consider that “spinning off” as much as cross-promotion.
Hill Street Blues spun off “Beverly Hills Buntz” which wasn’t a striking success but did last for a season.
“Beavis & Butthead” itself was a spinoff from an animation show called “Liquid Television”
Do reality shows count? “Road Rules” could be considered a spinoff of “The Real World” but even if it isn’t, the “Real World/Road Rules Challenge” must be. I think it’s also fair to consider “While You Were Out” as a spinoff of “Trading Spaces/Changing Rooms” (while “Surprise by Design” is not a spinoff but a ripoff).
Edith died between the 1st and 2nd seasons of “Archie Bunker’s Place.” What the finalé of “All in the Family” revealed was that she had a terminal illness. Reading through the episode guide there even appears to be a few episodes of ABP which featured her as the mainplayer.
The folks from Diff’rent Strokes visited McClean Stevenson in the pilot of “Hello Larry”
Here’s a good general reference on TV crossovers:
http://www.poobala.com/crossoverlist.html
This includes not just spinoffs but also cases where a character from one show did a one-time appearance on another show.
Wasn’t there a spin-off of Power Rangers where the hero wore a green insect-like costume? He only appeared in one episode of Power Rangers, and it was pretty obvious that they were introducing him just so they could spin him off. The spin-off didn’t seem to last very long. This was one of the earlier seasons of Rangers, while Zordon was still around.