For the most part, TV shows tell a story in chronological order. But there are the rare shows which develop a devoted fanbase due to their unique ability to tell a story out of order. Whether they offer up flashbacks, flashforwards, flash-sideways, or something else entirely, these TV programs keep fans entertained with their unique storytelling.
"Psych"
Most episodes of this USA comedy start with a flashback to Shawn's childhood, but many episodes also include flashbacks intercut throughout the middle of the episode or after the climax. For example, the fourth season episode " Shawn Takes a Shot in the Dark" includes multiple flashbacks throughout the episode. The Season 6 opener actually ends with a flashback, which shows how Shawn learned to beat a lie detector test from his father.
"Lost"
Few shows in TV history have ever showcased out-of-order storytelling as well as "Lost." With flashbacks, flashforwards, and alternate timelines, "Lost" constantly challenged viewers to draw their own conclusions about what was happening on the screen. By revealing backstories and possible futures for each character as slowly as possible (and out of order), the fans were drawn into the story in a way that probably wouldn't have been possible if the entire series was presented in chronological order.
To some long-time fans, the conceit behind "HIMYM" is starting to wear thin. However, many others are still enjoying the various flashbacks, forward jumps, and hilariously mis-remembered antics of Ted, Robin, Barney, Lily, and Marshall. The non-linear storytelling of this series offers plenty of opportunity for laughs and tears alike. But boy, Ted's kids from the flashforward segments must be getting pretty tired of sitting on that couch by now.
Given the fact that this series is all about time travel, it isn't surprising that many of the events take place in non-chronologial order. For example, the character River Song dies in her first appearance, and is seen as a baby in the episode that features her fifth appearance. As for the Doctor, he famously travels back through his own timeline three times during his attempts to save the universe in "The Big Bang." Also worth mentioning is the episode "Blink," which shows events from the 1920s, 1960s, and present-day all jumbled together.
Every episode of this modern fantasy series includes both scenes set in contemporary Storybrooke and scenes set in the "fairy tale world." These flashbacks don't appear in any sort of chronological order, but usually just relate to whichever character is central to the plot of the given episode.

