Marvel loved this trope in its earlier years. One of Nick Fury's Howling Commandoes was Dino Manelli, an Italian-American film star who was clearly not Dean Martin. And when Marvel briefly had the rights to Godzilla, SHIELD got a new special agent responsible for fixing the Helicarrier whose name was "Hugh Howards" (though nowadays it's usually Iron Man's father who plays the part of the Howard Hughes stand-in).
Phat was Eminem with superpowers, a secret upper class upbringing, and gay.
Henrietta Hunter was Princess Diana rewritten to be completely not Princess Diana because Marvel got cold feet. Perhaps intentionally, the story she appears in works a lot better knowing this than it does if you read it the way it was written.
Doctor Strange: Strange is Vincent Price. There's really no other way to say it. He only usually looks like Price (Strange began with a slight resemblance to Ming the Merciless, and his face is sometimes modeled on other actors), but his combination of portentous hamminess, erudition, and good humour is dead on for Price's persona.
The Warriors Three from The Mighty Thor are Errol Flynn, Charles Bronson, and, uh, Falstaff, except reimagined as Norse gods.
Many members of the Hellfire Club from X-Men visibly resemble and are named after celebrities who were famous at the time of their creation (which is rather fitting, given that historical hellfire clubs were supposedly where the influential and powerful went to debauch themselves). Just to use the obvious examples, Emma Frost is Diana Rigg, Sebastian Shaw is Robert Shaw, and recurring villain Mastermind became Peter Wyngarde just in time to join up.
Matt Fraction has said in interviews that Darla Deering/Miss Thing from FF is supposed to be Katy Perry if she were a superhero.
Warren Ellis's first issue has Tony interviewed by left-wing documentary-maker John Pillinger, who bears more than a passing resemblance to left-wing documentary maker John Pilger.
In a much later story Kieron Gillen introduces another left-wing journalist; an internet activist named Abigail Beryl Burns (with the online identity Red Peril) who is a Composite Character of Abigail Brady and Laurie Penny/Penny Red.
In the fourth-wall-averse series The Sensational She-Hulk, issue #12 revolves around a movie being made of She-Hulk's life:
She-Hulk: Shouldn't we be giving you a parody name or something? Like Mary Spleen? Mary Hart: Get real. Like we care if we're in a comic book.
Later in the same issue, it's revealed that Jen is going to be played in the biopic by the petite starlet "P. Isadora". Jen immediately lampshades the fact that her name got changed.
Spider-Man/Deadpool #6 is set during the making of a Deadpool movie starring a "Hollywood pretty-boy" named "Donald Dryans". Subverted when the story ends with Spidey declaring Deadpool should be played by a real actor, like Ryan Reynolds.
The Ultimates: Bruce Banner was having a self-esteem crisis and called his girlfriend Betty Ross, only to discover that she was dating Freddie Prinze Jr.. He turns into the Hulk and started to destroy everything in sight, while heading to the place where Betty and Freddie were having that date. Fortunately, Hulk never got anywhere near Freddie Prinze Jr. The Ultimates stopped him in time.
Amazing-Man from the All-Star Squadron is heavily based off Olympic athlete Jesse Owens.
While on the subject of Jack Kirby, Mister Miracle villain Funky Flashman was a publicity hogging sleazy businessman based partially on Stan Lee. Many fans believe this was a Take That! by Kirby after he left Marvel due to creative differences with Lee.
Mike Grell has stated that Tyroc from the Legion of Super-Heroes was inspired by actor and football player Fred "The Hammer" Williamson.
A psychologist shills his book on shows hosted by Harry Mann and Link Rambeau, parody versions of Larry King and Rush Limbaugh.
The Riddler takes talk show host Cassie Josie Rudolpho, basically a blonde Sally Jessy Raphael, and her audience hostage.
The Joker was shown killing two movie critics after they criticized the movie he was trying to make, but unlike the others no one bothered trying to hide the fact that the unnamed movie critics were basically Gene Siskel and Roger Ebert.
In one Chuck DixonRobin story, the Teen Wonder finds himself rescuing pop star Normandy Shields from a crazy stalker. It turns out she encouraged him in order to get more publicity.
Batman: The Dark Knight Returns was rife with these, containing caricatures of David Letterman ("David Endochrine"), Connie Chung ("Lola Chong"), Dr. Ruth Westheimer, and a nameless President that was obviously supposed to be Reagan. The Joker killed Letterman and Dr. Ruth.
The original Clayface is an actor named Basil Karlo (Boris Karloff).
In Batman Family #6, the first appearance of Duela Dent, the McGuffin is the final manuscript of mystery writer Christine Ariadne, creator of the detective Ulysses Pylate, an obvious reference to Agatha Christie, with a nod to her own Author Avatar, Ariadne Oliver.
The Oliver Twists in the 1970 story "Dead Til Proven Alive!" are The Beatles, complete with "Paul is Dead" conspiracy theory, with the twist that Paul's Expy turns out to be the only one who isn't dead.
Batman 80-Page Giant 2011 has one story in which the Riddler takes over a quiz show "in which the questions are answers and the answers are questions" called Imperilled!, hosted by Trey Alexander. Mixing things up a little, he also has a Lovely Assistant named Hannah Black.
A story featured various talk shows discussing Lex Luthor's apparent death. These included the sensationalist Ronaldo and the mawkish Susie Jamie Donatello.
In In Superman Annual #3, one of the annuals that was part of the Armageddon 2001 crossover event, President Herbert Forrest in a future timeline where Superman becomes a crusader against nuclear weapons bears a resemblance to President George H. W. Bush with Skunk Stripe hair. Furthermore, Herbert was President Bush's middle name and Forrest is a Pun on Bush. A version of him from another timeline in which he lost the 2000 presidential election to Superman is seen in Action Comics Annual #3.
Issue #355, "Momentus, Master of the Moon!": This issue came out in 1980, with a villain whose private identity is Dr Asa Ezaak. The villain has glasses, thick sideburns, and has published two hundred books on topics ranging from Astronomy to Zoology. The issue came out the year after noted science fact and Science Fiction author, Dr Isaac Asimov published Opus 200. He's also known for the muttonchop sideburns that "good doctor" Ezaak is drawn with.
Death Mayhew from the 1988 Blackhawk mini-series was very strongly based on Errol Flynn: a swashbuckling, Australian actor in Hollywood in the 1930s and 40s. However, Flynn's (falsely) suspected Nazi sympathies are exchanged for Mayhew being an out-and-out Nazi.
Teen Titans had the Citadel leader Lord Damyn supposedly inspired by real-life dictator Idi Amin.
During Denny O'Neil and Neal Adams' run on Green Lantern, the one-shot villains, Joshua and Senator Jeremiah Clutcher, were based on Charles Manson and Alabama Governor George C. Wallace, respectively.
2000 AD didn't even try to disguise B.L.A.I.R. 1 as anyone other than Tony Blair. Converted into a crimefighting cyborg with a built-in Robot Buddy called Doctor Spin, he used his hypnotic smile, super-strength and ability to take Spin's advice to make Britain great again by e.g. solving the unemployment crisis by sending single mothers down the coal mines.
Partway through Jack Kirby's Galactic Bounty Hunters, the action shifts to the life of comic book luminary Jack Berkley, a thinly-veiled Kirby stand-in. Note that the comic was co-written by Jack's daughter Lisa.
Cerebus: Even after outgrowing its Conan-parody beginning, the series continued to feature parody characters and thinly veiled celebrities, Lord Julius (Groucho Marx), Dirty Drew and Dirty Fleagle McGrew (Yosemite Sam) and Adam Weisshaupt (named after the historical figure credited with founding the Bavarian Illuminati). For extra efficiency, Dave Sim created an Elric parody and a Senator Claghorn/Foghorn Leghorn homage in the form of Elrod the Albino.
And on a meta level, two of the above characters, as well as Red Sophia (herself based on Red Sonja), and Astoria, are victims of this in-universe: Weisshaupt publishes a series of "Reads" that espouse his political agenda, with their names cleverly disguised as Red Sophina, Astonia, Lord Junius, and Cernebus.
The first two issues of IDW Publishing's ongoing feature a character named "Archie Maplin", obviously based on Charlie Chaplin. Chaplin himself was originally supposed to appear in the story, however the publishers were unable to get the rights from his estate. (While they didn't technically need the rights to use a Historical Domain Character, they belatedly realised they did need the rights to the fictional character he portrayed. The writer said in an interview that if they'd seen the problem sooner, they could have used Chaplin and not had him in costume.)
The Eleventh Doctor's companion, chameleonic glam rock star John Johns (aka Xavi Moonburst, the Tall Pale Earl), is obviously David Bowie.
Pulp Proto-Superhero "Dr. Coffin" was secretly Del Manning, a screen actor who did his own horrifying realistic monster makeup, earning himself the nickname "Man of 500 Faces". So basically Lon Chaney, Sr., if Chaney faked his death and became a vigilante.
Except when he's on the mountain; then he's Alan Moore.
Groucho from Dylan Dog. Yes, it's even the same name, even if it's known to be just an actor playing the part all the time (even when sleeping). And Dylan himself is a sosia of Rupert Everett. The author Sclavi is famous for rip-offs.
Dan Francisco in Judge Dredd rather resembles Barack Obama. During the "Mutants in Mega-City One" storyline, Rebellion even made "Vote Francisco - change we can believe in" campaign buttons.
This is very common in the Dreddverse. To list all the examples over the years would require its own page.
Robotech II The Sentinels: Dr. Emil Lang's character design had to be changed from his design in the original Macross series (where he appeared briefly). His Sentinels character design bears more than a passing resemblance to Charles Bronson. In one of the letters pages, the truth was revealed. Someone simply submitted a panel of Lang with a mustache drawn on him.
Lucas Lee of Scott Pilgrim is clearly based on JasonLee, in both name and appearance, and they are also both professional skateboarders who became actors.
The first issue feature the dictator Hassan Kussein (who's most definitely not Saddam Hussein) getting his head exploded.
And then there's the character Kirby, who's essentially Jack Kirby's head planted on a roided-up Cable body.
In Astro City, Shazam expy The Gentleman is modeled after Fred MacMurray (who has always been co-creator Alex Ross' model for Captain Marvel), while his sidekick Young Gentleman is modeled after Elvis Presley (a huge real-life fan of CM Junior), and his daughter Tillie is modeled after Judy Garland (in a nod to Mary Marvel originally being modeled after Garland.)
Destroyer Duck was written by Jack Kirby and Steve Gerber, who were in a legal battle with Marvel at the time due to creator's rights issues. One creator who notably turned up his nose at them for this was John Byrne, who happily described himself as a cog in the company. Coincidentally, one of the antagonists in the comic was the Cogburn, an entity created by the evil Mega-Corp to replace talented employees, that is noted to be extremely prideful of their nature as company men—but not only are they dumber than the employees they replace, they also have neither a spine nor genitalia.
In Silverblade, a séance is held in a haunted home led by a mysterious Native-American, Blackfeather. The ghost haunting the residence is the spirit of actor Brian Vane, who played a television super hero in the 1950s called the Winged Avenger. Vane suffered through career and personal problems before dying under mysterious circumstances, making the character a thinly-veiled stand-in for the story of The Adventures of Superman actor George Reeves.