Non-linear storytelling in TV series can be a powerful (and increasingly common) narrative device. This Is Us uses a combination of flashbacks and flashforwards to add emotional impact to the story of one family, Arrow spent its first five seasons using flashbacks in almost every episode to tell the story of the five years prior, and How To Get Away With Murder unspools each season's murder mystery with flash-forwards in each episode.
However, flashbacks in sitcoms are often used to very different effect. While some do use flashback scenes to drive the plot or reveal major secrets about the characters, the majority are used to greatest effect as a sight gag. The characters appear in outlandish costumes, or as more ridiculous past versions of themselves in flashbacks that can even also serve as cutaway gags.
Friends
Friends is a sitcom known for routinely using flashbacks - most often of Ross, Chandler, Rachel, and Monica when they were together in their late teens and early twenties. Ross and Chandler's college fashion choices are a big focus, along with Rachel's 'old' nose, and Monica when she was larger. However, these aren't the only flashbacks used, as the show also covers very recent events (Rachel bumping into Monica in the bar, Phoebe moving out), childhood incidents (Chandler's Thanksgiving), and even once covers a past life of Phoebe's!
Sometimes these flashbacks do serve to drive the plot (such as seeing how Chandler lost his toe), but most of the time they are purely comedic. Unfortunately, that comedy often relies on fat-phobic jokes at Monica's expense, too, which means that many of the flashbacks have become problematic over time.
Will & Grace
Will & Grace is another sitcom that starts at a point in time where the titular main characters already have a long history - and the audience accepts it, without going into the details too much. However, the show does use flashbacks in a very small number of episodes to show Will and Grace while they were dating.
The best-known flashback episode is 'Lows In The Mid-Eighties', a two-parter that focuses on Will and Grace in college. The episode does add depth to their backstory, and shows how their relationship has changed over the years. However, fans know that the best part of it is really the overblown '80s fashion and hairstyles, which are hilarious.
Gilmore Girls
Gilmore Girls doesn't involve many flashbacks, as the bulk of the show takes place in one timeline - and the focus is more on the fast-talking women in the present. However, there are a few flashback moments here, and they are all the more powerful for being unusual.
The few times that the show flashes back it is to Lorelai and Christopher as teens, when Lorelai found out she was pregnant, and later, when she left home. The flashbacks add depth to the relationship between Lorelai and Emily, and often make Emily more sympathetic - seeing her reaction to Lorelai leaving, and the way she stands up for her daughter, definitely helps shift her character away from the pure villain role of the early episodes.
New Girl
New Girl uses flashbacks in a very similar way to Friends - including the fat-suit. Flashbacks throughout the series are used to show Jess and Cece's friendship as children, Nick and Schmidt in college, and Winston and Nick as teens, as well as the occasional other expositionary flashbacks to various points in their lives.
While there is some interest in seeing how the characters met, or how they have changed, these flashbacks exist almost entirely as comic relief. Schmidt's size is used as a punchline (one of the more problematic aspects of the show), but Nick is also given braces, acne, and long greasy hair, and the rest of the gang are also given exaggerated appearances and mannerisms that are more about comedy than character.
Malcolm In The Middle
Malcolm in the Middle rarely uses flashbacks, but in season 2, the aptly titled 'Flashback' focuses on Lois, and the birth of each of her children. Each flashback shows the progression of her home, family, and character (including her appearance), and actually creates some real depth and sympathy for a character who can seem quite negatively stereotyped in the series as a whole.
Unlike many sitcom flashbacks, that focus on altered appearances for comedy's sake, these flashbacks show how Lois really changed, and it's a surprisingly sweet family moment.
The Big Bang Theory
The Big Bang Theory doesn't just use flashbacks, but also dream sequences (like Leonard in the Time Machine) or daydreams (Sheldon speed-running to the Grand Canyon to scream) to break up the linear narrative. The flashbacks themselves aren't too common in the show, sometimes showing the characters as children or teenagers, but the most effective flashbacks are those used to explain the gang's history - including some plot holes!
For many fans, the early seasons begged the question of why anyone would live with Sheldon, or hang out with him, or how the elevator got broken. Both questions, and more, are answered in flashback form - and given surprisingly heartwarming answers, too!
Crazy Ex Girlfriend
Crazy Ex Girlfriend is a series that intentionally steps away from the normal linear narrative, because its musical format means song and dance numbers in every episode. However, the series does include some more traditional flashbacks as well, and does so to incredible effect.
One of the most impressive things about the flashbacks in the series is the way that the color changes. Depending on Rebecca's mental state during the flashback, the color may be anywhere from bright and vibrant to almost entirely washed out or black and white. It's an incredibly effective way to convey mood and mental health without explicitly stating it. The flashbacks are also used to further the plot, rather than for comedy value (as the main timeline has more than enough wacky comedy in the musical numbers!). In the season 2 finale, for example, the flashbacks revealed how serious Rebecca's actions had been in the past - something that had a huge impact on the character, and the show going forward.
Fresh Off The Boat
Fresh Off The Boat is a perfect example of how to use shorter, sharper flashbacks as cutaway gags. Throughout the series, brief flashbacks are used to illustrate the story that one of the characters is telling, usually to hilarious effect. These are almost entirely used for comedic purposes, like when Evan celebrates his 'second 3rd birthday' in a flashback because Jessica is afraid of the number four.
The sitcom does an excellent job of including many flashbacks, but keeping them short and light enough that this adds to the overall series, rather than becoming overwhelming or clunky.
Golden Girls
Golden Girls follows the typical sitcom format of the time - episodes often feel like bottle episodes (due to the small cast and limited sets), often storylines from one episode don't follow on to the next, and flashbacks are few and far between. However, there are some flashbacks to when the women met each other, and several to when Dorothy and Sophia were much younger.
One of the most notable elements of these flashbacks is the casting - because Estelle Getty, who plays Sophia, was actually much younger than her character (she even wore makeup to make her look older), she is able to play her 'younger' self incredibly convincingly. In addition, Lynnie Green, who played a young Dorothy, was cast brilliantly - and Bea Arthur (Dorothy) was aged up to play Sophia's mother!
How I Met Your Mother
How I Met Your Mother uses flashbacks more than any other sitcom - because technically, almost the entire series takes place in flashback, as 'present day' Ted narrates the story to his children. Beyond this, there are flashbacks and flash-forwards within that timeline - everything from the character's childhoods to their college days to the near past to the far future is covered. This gets even more convoluted in the final season, when each episode jumps between the wedding, the run up to the wedding, and Ted's narration of the story.
This show is the epitome of a non-linear storytelling style, and it is done incredibly effectively. Dropped hints keep the audience guessing, flashbacks add comedy and character depth, and the narration and flashback style allow for unique comedic moments - like Ted forgetting a character's name, or the 'sandwiches' that they enjoy. It's incredibly complicated, but it works.