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.
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.
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.
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.
Friends. Although Chandler was more of a Deadpan Snarker, he was definitely the straight man to Joey. 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)
In Kenan & Kel, Kenan was this to Kel's funny man. Interestingly enough, All That shows that Kenan could also be the funny man, even before he got onto Saturday Night Live.
The comedic duo Mitchell and Web generally have Mitchell as the straight man.
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.
Monty Python's Flying Circus All of the members took turns being the straight man, if the sketch used one at all, and many of the sketches didn't 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.
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.
Larry on Perfect Strangers, although the dynamic changed after the 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.
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 punchline.
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.