A descendant of Vaudeville: an anthology of unrelated performances (be they musical, comedic, dramatic, etc.) by different performers. The first breakout television hits were variety shows, most notably the Texaco Star Theatre (hosted by Milton Berle) and The Ed Sullivan Show; other important examples from the '50s and '60s included The Red Skelton Show, The Jackie Gleason Show, The Carol Burnett Show, and The Smothers Brothers Comedy Hour. As you might notice, many such shows were named for the host(s).
This format fell out of favor in America in the early 1980s (although in Australia, Hey Hey Its Saturday lasted until 1999). Cable (particularly MTV and HBO) provided alternate outlets for the music, stand-up comedy, and miscellaneous acts that were the bread-and-butter of these shows, and viewers no longer had to sit through three acts they weren't interested in for the sake of one that they wanted to see. Also, tastes were becoming more polarized; whereas formerly people could endure musical styles they didn't care for much, more and more people actually HATED styles they disfavored.
Moreover, fatigue with the genre had sprung up in The '70s — Donny And Marie and Sonny and Cher were only the best-known examples in a decade that also brought us increasingly corny shows toplined by such acts as The Brady Bunch and the Bay City Rollers. One-shot and annual specials such as Circus of the Stars persisted into the early 1990s, but even those are now relatively rare.
Occasional attempts to revive the genre (on networks or cable) have been doomed to failure, though some might argue that Sketch Comedy shows such as Saturday Night Live, the late-night Talk Show format, and reality competitions such as American Idol and America's Got Talent keep the form on life support. NBC is giving it one more shot for the 2015-16 season with Neil Patrick Harris hosting Best Time Ever.
Producers of the British Sitcom The Young Ones booked a band for a guest appearance in every episode; musical performances qualified the series as a variety show, and it was therefore permitted a larger budget than usual for a BBC sitcom.
- Adam Hills In Gordon Street Tonight
- A radio example would be A Prairie Home Companion.
- Bill Nye Saves the World — In a sense. Each episode has a particular Central Theme that ties all the elements together, but within a single episode are contained any combination of live demonstrations in front of the audience, comedy sketches, "man on the street" style interviews, correspondent field pieces, panel discussions, and monologues from Bill himself.
- The Brady Bunch Hour
- The Carol Burnett Show
- Donny And Marie
- 1987's Dolly, starring Dolly Parton — it lasted one season and was considered a huge gamble even then.
- The Ed Sullivan Show
- Hee Haw sort of counts as one, albeit with a distinct rural appeal.
- Hey Hey Its Saturday
- The Hollywood Revue of 1929 was part of a series of filmed variety shows that were briefly in vogue during the 1928-30 era when sound films were new and novel. MGM, which was transitioning to talking films, simply put all of its stars into a variety show movie filled with unrelated sketches and songs. Warner Brothers did the exact same thing with its 1929 film The Show of Shows. 1930 film King of Jazz is a plotless variety show featuring Paul Waldman and his band in a series of lavish musical numbers, with sketch comedy interludes.
- The Muppet Show — Somewhere between a straight example and a spoof of this genre.
- As part of Newlyweds Nick And Jessica, Nick Lachey and Jessica Simpson did a variety show special on ABC in 2004 that flopped badly.
- In-universe in The Orbiting Human Circus (of the Air), the eponymous radio show's format includes musical numbers by bizarre animals and inanimate objects, novelty acts, and prerecorded spoken "true story" segments as closing "feature presentations."
- Pink Lady and Jeff — This 1980 NBC flop was the arguable Genre-Killer.
- Random Acts of Variety, an attempt at a revival
- Saturday Night Live originally had more of a variety show-style format, with multiple musical guests appearing in some early episodes and stand-up comedy mixed in with the sketch comedy.
- The Slammer — A variety show with a weird framing device.
- The Smothers Brothers Comedy Hour
- Solstrom — A 2003 Widget Series produced by Cirque du Soleil had whimsical fantasy storylines brought to life via a selection of circus/variety acts from both within and without Cirque's live shows.
- The Sonny and Cher Comedy Hour
- This Is Tom Jones
- The Tonight Show
- Viva Variety — Comedy Central's parody of these kinds of programs
- Technically, by having bands on, The Young Ones was considered a variety show. (This was because variety got a higher budget than light entertainment at the BBC.)