Xena is a spinoff of Hercules - but they tied at 6 seasons.
Another possibility is Transformers. The spinoff Beast Wars and its direct continuation, Beast Machines, lasted 5 seasons. Original show ran 5 (though, I think it may have run longer in Japan).
The original Alvin and the Chipmunks show was just one season. The followup 80s show was like 4 or 5 seasons.
Harvey Birdman: Attorney at Law has run longer than the original. Same deal with Space Ghost: Coast to Coast and the original cartoons.
Facts of Life ran longer than Diff'rent Strokes
Saved by the Bell ran MUCH longer than Good Morning, Miss Bliss
I believe She-Ra ran one season longer than He-Man. Both have a huge episode count for how long they ran though.
Viva La Bam has run longer than Jackass.
The Real Adventures of Jonny Quest did better than the original series.
Zoboomafoo ran longer than Kratt's Creatures.
Kung Fu: The Legend Continues ran a season longer than Kung Fu
The animated Mr. Bean got more episodes than the live action version.
The Munsters Today has more episodes than the Munsters.
My Little Pony and Friends had more eps than My little Pony Tales
Family Matters ran longer than Perfect Strangers
The Price Is Right's current incarnation has run WAY longer than the original. That's more of a sequel though.
Project Runway has surpassed Project Greenlight
Sam and Friends is the progenitor of the other muppet shows, which were much more popular. Sesame Street, Muppet Babies, and The Muppet Show.
Several Scooby Doo spinoffs have run longer than the original.
Sealab 2021 has run much longer than the original.
ALL the Star Trek spinoffs did much better than the original, discounting the Animated Series.
What-a-Cartoon Show was Cartoon Networks deliberate attempt to make animated characters snipoff, as it was a short showcase. Johnny Bravo, Dexter's Laboratory, Cow and Chicken, and the Power Puff GIrls all ran longer than the original show.
Most of these I got from
http://en.wikipedia.org/wiki/List_of_television_spin-offs.
Sorry, excited about Christmas and couldn't sleep!