Bleach: Happens a lot in the manga. They often happen during a significant fight in which one character is going to lose or die or if the fight helps defines a character that's won. The anime, via Adaptation Expansion, can go to town with this making episodes out of what's sometimes nothing more than a few panels in the manga.
Cluster Edge uses this constantly, to the point it conquers the series.
Happens multiple times in Code Geass where characters' childhoods are shown to better explain their motivations and behavior. Usually it leads to a Tear Jerker.
Episodes of the Detective Conan anime adapted from the manga, especially multi-part episodes, frequently employ flashbacks and in-dialogue recaps to pad out the run time (as well as occasionally replaying the last several minutes of the previous episode as the beginning of the current one), since otherwise there wouldn't be enough material to fill the full episode length. It's not uncommon to have seen the same footage 3 or 4 times (counting the first time it was shown) by the end of a multi-part episode. (It's especially noticeable when viewing all parts of multi-part episodes in one sitting.)
In Digimon, after Impmon does his HeelFace Turn, the series constantly flashes back to Leomon's death, which Impmon caused as Beelzemon and comes to deeply regret. Impmon and Jeri have other flashbacks to show how they became what they are. Jeri's mother died when she was little, her father became distant and she could never really connect with her step-mom, and Impmon gained a hatred of humans because of his abuse at the hands of his young Tamers.
Series one and two also had flashbacks. Most of the Digidestined have flashbacks of family deaths, such as Izzy and Cody, who have flashbacks about their parents' deaths, Ken has his brother Sam's death, and Tai has the time that he almost was responsible for his sister Kari's demise. Owikowa also had flashbacks, to show how and Hiroki (Cody's dad) were friends, and how alone he felt after Hiroki died. TK often has flashbacks about Angemon's sacrifice to stop Devimon, and Ken has flashbacks of his time as the Digimon Emperor.
Gintama is not the typical shounen series where characters grow and get stronger as the story progresses. Instead they start strong and stay strong, and goofy, and vulgar, and undignified. The majority of the funny stuff happens in the present. It's in the flashbacks, however, that the serious pasts of the main characters come out (with some funny moments) to show what happened to bring these characters here to the present. Eventually, the drama of the past catches up to the drama of the present.
Hayate the Combat Butler uses flashbacks to explain some parts of a few character traits, then spends an arc to build up a new character and ready the story to be thrown into a much more serious arc, before toning things back down.
THE iDOLM@STER - Chihaya gets a ton of flashbacks foreshadowing her past, before things hit the fan.
The beginning of episode 9 of Is the Order a Rabbit? shows Chino's grandfather while he was still human sitting on a park bench with his pet rabbit Tippy. He then sees a young Cocoa who sits next to him while hugging Tippy, and her older sister Mocha can be seen as she leaves the bench a short while later.
Kiddy Grade starts doing frequent Flashback Cuts around episodes 9-12 when Eclair struggles with her repressed memories and the numerous times she's come back from the dead. This is followed by episode 16, appropriately titled "Look/Back" which combines a Recap Episode with expository flashbacks and episode 20 which is again largely based around a series of flashbacks.
Naruto has an large number of flashbacks. Protagonists, antagonists, and bystanders alike will go into flashback after flashback, explaining their tragic back-stories, lives, and motives. Entire episodes will consist two characters talking while they exchange flashbacks. An example: Hinata's confession to Naruto during the Pein arc took a couple pages in the manga, while in the anime it took an episode because roughly 3/4 of the episode was a montage of flashbacks going through her childhood and her interactions with Naruto. This used to be different with this series in its early days, when it didn't have much to recount, but the anime Overtook the Manga and went into a Filler marathon until the manga picked back up again. Then the producers of the anime developed a strategy to add Padding to almost all canon episodes so they would be as drawn out as possible, barring extended fight scenes, lest this happen again. Many times these flashbacks really accentuate a moment or decision by a character. Example: Sasuke's Tragic Backstory at the Valley of the End, to which we get new meanings of hundreds of chapters later. In the case of Hinata's flashbacks in the anime episode of the Pain arc, the flashbacks were not mere filler but an elaboration of Naruto and Hinata's characters, or an expansion on what is canon.
Ninin Ga Shinobuden parodies this. When asked to explain how he got stuck on Miyabi's chest, Onsokumaru promptly goes into a flashback covering various events from the previous week, even though the only relevant event (Miyabi tripping and falling on top of him) occurred about five minutes earlier. The ninja are quick to point this out.
One Piece uses these like there's no tomorrow. Mostly for the background stories of the main cast, but other characters get plenty of them, too.
The Rave Master dub as a truly epic flashback. The first time they use it it's a little fitting; It shows when Elie first meets Sieg after developing amnesia and he attempts to kill her, leading to her present actions. The second time they play it is right after she meets Sieg again. Right before it starts he questions her with (voiced very well) "How did you survive?" Then it goes to the flashback, where he says the exact same thing... in the exact same tone, with the exact same expression (not that he has that many expressions)
Soul Eater - Used mostly in the conventional manner of revealing backstory, but Maka's one during the Clown chapters is particularly twisted. It looks like an ordinary flashback until everyone falls down dead and little!Maka wants to know why her daddy isn't getting up...
Tenjho Tenge has a flashback arc, which takes up a large chunk of the anime. While it is important for establishing the backstories of many of the show's characters, unfortunately the anime didn't get far enough to really do anything with those newly fleshed-out characters before it was cancelled.
A lot of these show up in Yu-Gi-Oh!, even to the point where they actually had a Flashback within a Flashback.
Used regularly in Unlimited Fafnir to reveal important events, such as Yuu first making a contract with Yggdrasil for Power at a Price way to defeat a dragon attacking his hometown.