Monty Python's Flying Circus often subverts this by making the Straight Man even stranger. A recurring character called The Colonel often served this role, shutting down a sketch partway through because he felt that he hadn't delivered a single funny line.
John Cleese is the straightest man in the world, even when what he's doing is ridiculous ("Ministry of Silly Walks").
Averted after the first season or so, as Larry's wacky schemes ended up driving the plots more and more often. By the time the show ended, both characters were getting an equal number of gags. Still, Larry's original job as straight man got lampshaded near the end of the series in an Imagine Spot where Balki and he play Laurel and Hardy, respectively.
Oscar is usually the Straight Man to Felix on The Odd Couple, except when the joke is based on Oscar's messy habits; then the roles are reversed.
On The Daily Show, Jon Stewart plays the straight man to the various fake correspondents, who themselves tend to conduct interviews where they make their subjects unwitting straight men. Stewart also uses footage (sometimes out of context) and reports of various politicians, newmakers and media whores as straight men for his own punchlines, but it could be argued that sometimes what they are doing is so outrageous that he can only react as an incredulous straight man even for them.
Stewart also plays the straight man to Stephen Colbert whenever he does tosses over to Colbert's show.
From the second series onwards, Rowan Atkinson's portrayal of Blackadder was more or less a straight man for the characters of Baldrick, Percy and George. Except when he was saying something snarky.
Burton "Gus" Guster is Straight Man to Shawn Spencer on Psych.
The title of straight man is passed around to everyone that isn't Shawn, as Gus is part of Shawn's jokes as often as he's Straight man to them. In those cases usually the straight man reverts to Lassie or Shawn's dad.
This gets used a lot in the shows Yes, Minister and Yes, Prime Minister. Essentially, Hacker and Humphrey are both playing the Straight Man role to Bernard. The actor who played Bernard has even gone so far as to say in an interview that, though his role was technically the most minor of the three main roles, he feels that he got the best job, because Hacker and Humphrey would often have extremely long sections of memorized, straight dialogue (which, given Humphrey's penchant for Sesquipedalian Loquaciousness, is all the more impressive) before he jumped in with a short, but often hilarious, punchline.
Castiel on Supernatural, especially in Season 5. He doesn't understand when the other characters are being funny and/or sarcastic, which makes his sincere replies hilariously adorable.
In earlier seasons, Sam often played the Straight Man to Dean.
The calm, introspective Sargeant Wilson was straight man to the bombastic Captain Mainwearing on Dad's Army, another WWII English sitcom (this time about the Home Guard).
On The Big Bang Theory, Johnny Galecki's character Leonard plays this role, largely for Sheldon's comic lines, and sometimes for funny lines from other characters as well. In Galecki's much smaller recurring character role on Roseanne, his character David tended to play this role for Darlene and others, as well.
Friends. Although Chandler was more of a Deadpan Snarker, he was definitely the straight man to Joey's foil. In one case, he was able to pull it off without even saying anything, as the group prepared to head to London:
Chandler: You got your passport? Joey: Yeah, in the third drawer of my dresser. Wouldn't want to lose that. Chandler: (just stares at him) Joey: ...oh! (runs back to his room)
Jim, Pam, Toby, Stanley, and Oscar on The Office (US) all serve as as Straight Man/Woman to the wackiness that emanates from various corners of the office. Jim in particular balance the insanity that is Michael Scott and Dwight Schrute.
Carly in iCarly. Carly is something of a "Jerry Seinfeld" example, as the show is named after her. Carly provides the setup for most of Spencer and Sam's jokes. Her main comedic role is to deliver rejections to Dogged Nice Guy Freddie, who has a crush on her. Even so, half the time Sam delivers them instead.
After Mark leaves, the dynamic changes. Ann is still the general comic foil, but as April's apathetic snark gets softer she moves in to become the foil to Andy, and Leslie herself ends up acting as the straight woman to the whole office when they get too wacky. Also, Donna has her moments.
And later Ben comes in to be the straight man to practically everyone, but mostly to Leslie, Chris and Tom.
In the classic series: Apollo and Boomer both play this to Starbuck, but the real honor goes to Colonal Tigh.
In the reimagined series: Tigh is the most notable example but Laura Roslin and Bill Adama can be this as well. Honestly, just about anyone on the show became the straight man when Baltar was making excuses.
In the first and second season of Angel, Angel often played the straight man to Cordelia and Wesley, although Wesley would sometimes play the Straight Man himself in exchanges with Cordelia. Then in Season 5, when Cordy left the show, Angel got to play the Straight Man to Spike.
Greg to his wife especially, and the rest of the cast in general in Dharma and Greg. Lampshaded a few times.
Britta on Community has a reputation as a buzzkill.
Or at least her initial characterization was. By season 3, she's one of the ditziest characters in the group, and more often than not, Jeff plays the sarcastic straight man to her increasingly manic hijinks. Though the study group as a whole has been in the position of straight man to another member of the group at some point (except Abed and Pierce)
Deborah on Everybody Loves Raymond acts as the comic foil to Raymond and his quirky family. Patricia Heaton can sometimes steal the scene by just standing there and saying nothing. Body language conveys it all.
Michael Bluth on Arrested Development is this combined with Only Sane Man. His attempts to manage his completely and utterly insane family of narcissists lead to much of the comedy. His son George Michael and niece Maeby fall into this trope much of the time as well. Michael is, however, also a deconstruction of the trope: despite the "ordinary guy" facade he puts on, his interactions with George Michael show him to be as uptight and completely intolerant of casualness as his family says. He is also repeatedly shown to actually being incredibly gullible in that he often trusts his family members far too much for people who has repeatedly fail to live up to even his lowest expectations.
George Fenneman, The Announcer on You Bet Your Life, was called "the male Margaret Dumont," by Groucho Marx. As she was the comedian's greatest comedic foil, Fenneman was deeply flattered by the comparison.
The Young Ones has Mike, who is the least involved in the slapstick (and receives by far the least physical blows) and most of his humour comes from making lame jokes, his "cool" attitude, and his many shady business practices. However, he is also the closest the lads have to a "leader" and facilitates several of the jokes, despite being considered bland.
Subverted with Captain Holt in Brooklyn Nine-Nine, who initially seems like the deadpan, serious and down-to-earth commander forced to manage a squad of rowdy, eccentric detectives in a similar fashion to Barney Miller. In fact, he has plenty of quirks himself, and his deadpan seriousness frequently makes him come across as far stranger than any of his detectives, who frequently find themselves bewildered foils to his robotic weirdness. While none of the detectives are exactly without their quirks, the Straight Man is actually far more likely to be Sgt. Jeffords, who (once he gets over his fear of being in the field) is comparatively normal and frequently the Only Sane Man and Only Sane Employee.
During his time on Monday Night Football; Frank Gifford filled this role in his commentary, particularly in the early years alongside Howard Cosell and Don Meredith but this continued later on with Al Michaels and Dan Dierdorf.