You can count Star Trek, depending upon how you define the premise. Star Trek had two series, a live action show and an animated one. The animated can also be considered a spin-off, depending upon how you define it. There were 4 other spin-off series. DS has had two incarnations, three if you count the unsold pilot. Four, if you are counting the films. If you are going to count the numbers of spin-offs, then All in the Family and Mary Tyler Moore both have quite a ffew. If you are looking at sequel series, using most of the same cast, or remakes using the familiar characters then you have a different situation. THe Brady Bunch, as mentioned in an earlier post has the record there. Wasn't there a pilot film for a series wth Mike Brady as president??? This one used the movie cast, if i remember correctly. I did not see it, so I might be WAYYY off.
In terms of licensing, DS was the leader for many years. With 32 novels, it beat both Trek and Doctor Who for a long time. I'm diffrentiating novels containing new stories from novelizations of episodes or movies. Trek had the record for that for a while. Doctor Who surpassed them eventually, with the Target novelizations.
As far as audio adventures go, assuming they are using a significant number of original players, as is the case with DS and Who, I've always believed that these should be consideredd a legitimate continuation of the show, providing they are licensed and fit the continuty. On that basis, Doctor Who also has the Bernice Summerfield Adventures, The Dalek Empire and Cybermen mini-series, the Sarah Jane Smith Adventures, and a few odds and ends.
If you are just counting TV, does that include animation? Shows like the Flintstones, Scooby Doo, and others have had innumerable incarntations.
Dragnet had three series, 50s, 60s and recently.
The Munsters had two series and a pilot for a third.
The Addams Family had a prime-time show and at least two animated series, a Hallloween special/pilot in the 70s, and two movies.
DS is high on the list of cult shows that refuse to go away. How high depends upon the fine print in the definition.
In terms of novels, besides Trek and Who, does any other show exceed 35?