The 1950 musical Call Me Madam starred Ethel Merman as Mrs. Sally Adams, America's ambassador to the small Ruritanian country of Lichtenburg (famous for its cheese); this was roughly based on Perle Mesta, Harry Truman's ambassador to Luxembourg. The original program disclaimed that "neither the character of Mrs. Sally Adams nor Miss Ethel Merman resemble[s] any person living or dead," and also played with No Communities Were Harmed by referring to Lichtenburg and the United States of America as "two mythical countries."
In Victorian times, W.H. Smith - now best known for the chain of stores - was promoted to First Lord of Britain's Navy, despite knowing little or nothing about ships. When Gilbert and Sullivan were writing H.M.S. Pinafore, Gilbert, setting out the plot for Sullivan, wrote about a song for "the First Lord ? tracing his career as office-boy in [a] cotton-broker's office, clerk, traveller, junior partner and First Lord of Britain's Navy.... Of course there will be no personality in this - the fact that the First Lord in the Opera is a Radical of the most pronounced type will do away with any suspicion that W. H. Smith is intended." Actually, everyone presumed Smith was intended (as Gilbert probably knew full well they would), to the point of him living out the rest of his life with the nickname "Pinafore Smith".
Another Gilbert and Sullivan example: the fleshly poet Reginald Bunthorne in Patience was modeled on Oscar Wilde, to the point that D'Oyly Carte had lecture appearances by him in American cities where Patience was touring so that theatergoers could recognize what the play was parodying.
In The Man Who Came to Dinner, the (speaking) character of Banjo is based on Harpo Marx (his Hollywood co-stars are named as Wacko and Sloppo). Sheridan Whiteside was largely modeled on the Alter-Ego Acting persona of Alexander Woollcott (to whom the play was dedicated by its authors "for reasons that are nobody's business") Lorraine Sheldon represents English actress Gertrude Lawrence, and Beverly Carlton is a thinly veiled pastiche of playwright and wit NoŽl Coward.
Another fictionalized version of Noel Coward is Eric Dare from the little-known Cole Porter musical Jubilee. In the same show, Eva Standing could practically have been a pseudonym for Elsa Maxwell; Charles "Mowgli" Rausmiller, however, is more a parody of Tarzan than of Johnny Weissmuller.
Finian's Rainbow: It's probably not a coincidence that Woody Mahoney, union organizer, folk singer (whose shame it is that he can't play the guitar he's carrying), and enemy of finance men, has the same first name as Woody Guthrie. (At one point, Woody is supposed to speak "in a 'Talking Union Blues' rhythm.")
Freddie Trumper, the Jerk Ass American chess player in Chess, is supposed to be a Bobby Fischer expy, with some characteristics of John McEnroe (whom Freddie refers to as "that tennis player—what's his name"). The Russian player, Anatoly Sergievsky, was initially based on Boris Spassky but the resemblance decreased every time the musical was rewritten.
Of Thee I Sing: Apparently, some reviews of the original production noticed a resemblance between John P. Wintergreen (as played by William Gaxton) and Jimmy Walker, then mayor of New York City (and part-time songwriter), which may have been denied. All but openly acknowledged, though, was that all nine Supreme Court Judges were made up like Oliver Wendell Holmes.
In Arthur Miller's play After the Fall, Maggie has a highly suspicious resemblance to the author's late ex-wife, Marilyn Monroe.
I Just Stopped By To See The Man by Stephen Jeffreys consists of a meeting between No Celebrities Were Harmed versions of Robert Johnson (if he'd lived until the sixties), Angela Davis, and Jimmy Page.
Ira Levin's play Critic's Choice has a drama critic married to a playwright, like Walter and Jean Kerr were in Real Life.
Ethan Kane in Sex with Strangers, who runs the eponymous blog about picking up women in bars, is a thinly veiled version of Tucker Max.
In The Doughgirls by Joseph Fields, Sergeant Natalia Chodorov is based on Lyudmila Pavlichenko, though her last name is obviously that of Fields's frequent co-writer, Jerome Chodorov.
The 2014-2015 British play Great Britain is based around the rise and fall of the News of the World, the British tabloid paper. As such, most of the characters, in particular those working for the Free Press, are very heavily based off the various real-life paper, with a Rupert Murdoch substitute (though his nationality is changed from Australian to Irish with implied links to the NRA), an older version of David Cameron with a different name and various officers in the Metropolitan Police. Notably, however, the knockoff version of Rebekah Brooks is treated in a much more sympathetic light, in no small part due to the fact that she was legally declared innocent by the British courts in real life.
Alison's House: The posthumous character of Alison Stanhope is a very thinly veiled Emily Dickinson. Playwright Susan Glaspell actually sought to write a play about Dickinson, for the centenary of her birth in 1930. But Dickinson's works and the rights to her story were still under control of the estate at the time, and the surviving Dickinsons refused Glaspell permission to use Emily Dickinson's name or her poetry. Alison and her Real Life counterpart were both shut-ins for years. Both had an easy rapport with the children of the family despite being socially reclusive. Both wrote reams of poetry that weren't published until after they died. Both had sisters that also never married (Dickinson's sister was named Lavinia) and both asked that sister to destroy her unpublished works after her death. And while it is unknown if Emily Dickinson had a forbidden love of the sort that Alison Stanhope had in the backstory, the "Master letters" have often been interpreted in that way.