On “The Drew Carey Show”, Drew Carey, a real-life middle-class schlub from Cleveland, played Drew Carey, a fictional middle-class schlub from Cleveland.
Just saw Dr Joyce Brothers playing herself on Taxi. Come to think of it, she played herself on ***Frasier ***too.
If we are including The Simpsons, then I guess we have to include Futurama who had fictional versions(or at least their heads) of numerous living people including Al Gore, the Beastie Boys, the cast of Star Trek(though I believe Welshie was an original character), and Beck.
In one episode of the 1990s “WKRP” reboot, there was a ‘controversial right-wing’ talk show host by the name of ‘Lash Rambo.’
Both examples where the actors were given permission to continue to play their fictional characters in real life.
Rush Limbaugh voiced himself on at least one episode of Family Guy.
First, I would interpret the question to mean the main characters. Therefore, I would include everything from The Goldbergs to Seinfeld. However, I would exclude one-shot or limited cameos such as Isabella Rossellini on Friends or Lou Ferrigno on King of Queens.
There are many examples posted already. Here are a few more.
Bull is based on Dr Phil [McGraw], who was a prominent Jury Consultant before his TV show. Lie to Me was based on Paul Ekman. Kojak (including the TV movie The Marcus-Nelson Murders) was a composite of several real people. Berreta/Toma was based on a real New Jersey cop.
In the 1950s (when I was a kid) TV was full of Westerns including Wyatt Earp and Wild Bill Hickok. There also was a British import about Robin Hood. Does that count as a real person? I say yes, but am open to discussion.
The thread is about living persons being portrayed, which pretty much eliminates Wyatt Earp, Wild Bill Hickock and, especially, Robin Hood.
The first film about Wild Bill Hickock titled Wild Bill Hickok was released in 1923. Wyatt Earp was a character in it played by Bert Lindley. It’s the only film that portrayed Wyatt Earp while Earp was still alive. (Earp died in 1929.)
Louie Anderson did the same with the cartoon “Life with Louie”
Off topic Goldbergs post: in the Highlander Club episode the club adviser (shop teacher) is/was played by Clancy Brown (Kurgan in the movie) and he broke into the voice a few times. I enjoyed it (he does mention “the misunderstood Kurgan”)
Brian
One that hasn’t been mentioned: The Dick Van Dyke Show was based on series creator (and Alan Brady portrayer) Carl Reiner’s work in television.
Post #42, I believe.
A really weird one was when Mork met Robin Williams on Mork & Mindy. “Robin” let Mork realize that fame wasn’t all it was cracked up to be. I suppose reruns of that ep would seem especially sad after Robin’s suicide decades later.
Also the time Mr. T was filming something or else (an A-Team scene?) using the Drummends’ apartment as a location for some reason.
Very interesting
The lions were played by stunt-double though. 
Seriously, President George W Bush was portrayed on the pilot episode of NCIS. As I mentioned up-thread, First Lady Michelle Obama made a cameo as herself on a later episode.
Slight hijack, but I’ve really been enjoying this first season of The Kids Are Alright. I recommend it. (I also enjoy The Goldbergs, but enjoyed it more in the first couple of seasons.)
Peter Lind Hays and Mary Healy were in several shows where they played fictionalized versions of themselves.
Bob had the character of Harlan Stone, who was clearly modeled on Harlan Ellison.
The Duck Factory, about an animated studio, had a voice actor who was played by and clearly modeled on Don Messick. Staff writer Marty Fenneman was played by Jay Tarses, who was best known as a comedy writer.
There was a cartoon called Lil Rosie which was a highly fictionalized account of Roseanne Barr’s childhood.
I’m not sure it counts but Yellow Submarine also featured four voice actors doing the voices of the Sgt. Peppers Lonely Hearts Club Band which was a fictional version of the Fab Four.