I liked the "It's Punky Brewster" cartoon! In fact, I grew up watching that cartoon and didn't even know a live action version existed until many years later. I still haven't seen the live action version! However, when I get some money I've been wanting to get the Season DVDs for the live action Punky Brewster show, which do come with a few hours worth of the cartoon, by the way.
There definitely was the Fraggle Rock cartoon and there was actually 2 ALF cartoons. There was one just called "ALF", which revolved around Gordon Shumway's adventures of Melmac with his family and Skip and Rhonda before Melmac exploded. There was also a later series called "ALF Tales", which had ALF and family and friends acting out fairy tales. I used to watch both, as well as the original live action ALF series. They're all great.
Live action shows and movies inspiring cartoons could be a whole new category. Here's a few more I can think of off hand. The Back to the Future trilogy of movies brought a really great cartoon series called "Back to the Future". (It ran from about 1991-2 or so and did have live action segments with Christopher Lloyd as Doc and Bill Nye, the Science Guy as his assistant.)
Then there's the Teen Wolf movies and the Teen Wolf cartoon, which I used to catch some of. It's not too bad.
And of course, the 7 Police Academy movies (possibly 8 by next year) had a great Police Academy cartoon series running from about 1988 I think through the early 90s.
Bill and Ted's Excellent Adventure inspired both a cartoon and live action series in the early 90s. I never saw the live action version, but I definitely remember watching the cartoon and it was quite good.
Of course, the Ghostbusters movies inspired "The Real Ghostbusters" cartoon. (I have to differentiate because there was a live action Ghostbusters show in the late 70s as well a different Ghostbusters cartoon in the early 80s. Neither one had anything to do with the 2 live action Ghostbusters movies.)
A couple of earlier examples also include "The Planet of the Apes" movies, which inspired both a 1974 live action series and a cartoon series called "Return to the Planet of the Apes" in the late 70s.
And from the Happy Days show and its spinoffs, we have the "Fonz and the Happy Days Gang" cartoon show, "Laverne and Shirley in the Army" cartoon, and a "Mork and Mindy" cartoon.
Gilligan's Island also inspired a cartoon called "Gilligan's Planet"!
I don't know if this exactly counts, but there was a cartoon in the 80s called "Bionic Six", which looks like it might have been inspired by The Six Million Dollar Man and The Bionic Woman, even though neither character was actually in the cartoon.
You could also say that the Batman cartoons on in the late 60s and the newer one in 1977 were inspired by the success of the 1966-1968 live action Batman show, seeing as how Adam West and Burt Ward voiced the characters.
And of course, the "Droids", "Ewoks", and "Star Wars: Clone Wars" are all cartoons inspired from the Star Wars movies.
In 1973-1974, there was a cartoon version of Star Trek, starring most of the original voices of the original series. The cartoon was an animated version of the original series with Captain Kirk and crew.
Jim Carrey has actually had a few cartoon series inspired by his movies. One of the biggest ones would be "The Mask" cartoon, inspired by the 1994 movie "The Mask". I used to watch this cartoon some. He also had another big hit in 1994 with "Ace Ventura: Pet Detective" and there was an "Ace Ventura" cartoon series as well, right around 1994-1995. In this same time period, he had one other cartoon series made for one of his biggest hits and one of my brother's and my favorite movies, "Dumb and Dumber". The "Dumb and Dumber" cartoon was rather short-lived, but it was around for a while around 1994 and 1995.
Also, coming originally from a trading card series and a 1987 live action movie, there was also a 1988 cartoon series called "Garbage Pail Kids". I used to watch this cartoon as well, and though banned in America, it's actually not nearly as bad as you might think. It was actually quite clean (well, not too clean since they were coming out of the garbage pail and all
) and pretty funny.
I should also mention that there's been both 2 live action movies and a cartoon series of "Men in Black".
And there was also a cartoon at least somewhat inspired by the success of The A-Team. One of the main stars, Mr. T had a cartoon called "Mr. T", which featured Mr. T in live action scenes as well as a cartoon adventure of him and some kids who I think were gymnasts or something. They had lots of adventures, of course. Technically, the "Mr. T" cartoon did not feature the character of B.A. Baracus, so it wasn't a cartoon version of "The A-Team", but the "Mr. T" cartoon only came about because of the huge success of Mr. T on The A-Team.
The only other example I can think of this off hand is the Macaulay Culkin cartoon "Wish Kid", though I'm not sure that Culkin was actually in the cartoon as himself.
And then there's also the "Harlem Globetrotters" cartoon. They also met Scooby Doo three times on The Scooby Doo Movie Mysteries series.
The 1964 live action series The Addams Family also inspired both a late 1970s cartoon (there was also an episode where they met Scooby Doo and the gang on The Scooby Doo Movie Mysteries series). There was also a cartoon series for The Addams Family in the late 80s-early 90s. Somewhere in the early 90s, there was also a cartoon based on the 1988 movie Beetlejuice. There was also a cartoon version of Beethoven, based on the 1992 movie of the same name about the St. Bernard dog.
I'm sure there's probably even more than this that I've forgotten. Like the episode of "The Scooby Doo Movie Mysteries" where he met Jeannie, from "I Dream of Jeannie". I don't know that any cartoon version was done of that show, beyond that one appearance. Okay, well someone else add to the list. I've rambled on long enough now.