The show had an entire vacation Story Arc that ate most of the fourth season and leaked into the fifth. It pretty much inflated every aspect of this trope to fit — especially, since it was a trip to Hollywood, the Special Guest part.
Also later in the fifth season, the tour through Europe.
Family Ties has the TV movie Family Ties Vacation where the Keatons went to England*
(the movie has not, apparently, been shown in the UK due to Channel Four not running the entire series)
Subversion: one entire episode was built around the family stuck in a traffic jam on their way to the vacation.
Played Straight: the previous episode was them at a water park. The traffic jam episode was the drive home. And the B-plot with Dewie was a 2-parter.
Another played straight, but also played 'with': Malcolm and Reese try to snealk off to 'Burning Man' only to be caught by their parents...who decide it sounds like a delightful family vacation. Reese embraces the spirit of Burning Man, Lois does to yet still acts like its a family fun time, Malcolm gets into it in a sense but can't completely let go, Hal tries to act like its any other vacation but his conservative nature and hatred of the free spirited nature of the festival makes him hole up in the RV (the other people thinking he's making a live art piece about pretenciousness, and Dewey....is forced to do everything Hal doesn't want to.
Sesame Street had a series of episodes where the characters went to Puerto Rico to visit Maria's family. Also, there were one-hour specials like Big Bird in China and Big Bird in Japan.
Roseanne had an episode where Dan and Roseanne go to Vegas, featuring nonstop gambling and a visit with Wayne Newton (and a Wayne Newton impersonator). Another episode featured a trip to Walt Disney World.
In season 3 of Boy Meets World, Topanga wins a trip to Disney World. Cory follows her to make up with her.
Step by Step had two of these: one in Hawaii and one at Disney World.
The Monkees episode "The Monkees in Paris" where the guys walk off the set tired of the same old scripts and go to Paris.
Gossip Girl season four sees Blair and Serena enjoy their summer vacation in Paris.
Subverted in a first season episode of Criminal Minds. It starts with the team getting time off and Elle and Morgan going to Jamaica (?). They promptly discover a dead body and the rest of the team is called in.
Home Improvement had two, one where the Taylor family goes to a lake house, and one where Tim, Jill, Al, Heidi and Wilson go on a rafting trip for Tim's birthday.
Late Show With David Letterman spent a week in London (which also marked the only time the series has seen the light of British terrestrial television - BBC2 aired those episodes). Johnny Carson and Bill Maher also had UK jaunts.
Steve and the kids win a trip to Universal Studios Orlando on The Steve Harvey Show. Regina tags along because she's always wanted to ride The Hulk rollercoaster, and Cedric uses the trip to give Lovita a honeymoon.
In the second-season 2 Broke Girls episode "And the Bear Problem", Caroline, Max and Andy go on a weekend trip to a cabin.
Episode 3 of Llamas with Hats: Carl enjoys himself rather more than Paul does...
The Ni Hao Kai Lan episode, "Ni Hao's Trip to China" is a textbook example. It's a double-length episode where everyone visits Kai-lan's great-aunt in China, tries various new things, and meet a newborn baby panda.
American Dragon Jake Long: Jake Long will always have some magical emergency even during what would otherwise be vacation episodes.
"The Long Weekend": His Dad took him into a camping trip, where Jake ended up having to save a village of sprites.
"Feeding Frenzy": The Longs were visiting relatives in Florida and a gang of magical sharks caused mayhem.
"The Hong Kong Longs": The Longs went to Hong Kong for a two-week vacation. It was also the time for all dragons on Earth to meet at Victoria Peak and the Dark Dragon captured Lao Shi to force Jake to slip a mind-controlling potion to control all dragons. This was also the only episode of the series to have no scene in America.