They say that there's no point in regretting the past, but that doesn't stop these anime characters. To be fair, it would be hard not to feel remorse after the horrific consequences that some of these characters had to face as a result of their choices.
Edward and Alphonse Elric of Fullmetal Alchemist serve as a classic example of this trope - they tried to bring their mother back to life using alchemy, and nearly lost their own lives in the process. Other anime characters who regretted their decisions don't have to deal with something as serious as that. Yamato Kurosawa of Say "I Love You" regretted being callous with his girlfriend Mei, but was able to make up for it with an apology and changed behavior.
Whatever the outcome, it's interesting to watch anime heroes make the wrong choice. Imperfection is human, and it creates conflict that drives the story. Which mistake did you find the most compelling?
This trope is actually one of the main themes of Fullmetal Alchemist. When Edward and Alphonse Elric lose their mother to an unknown disease, they decide that they aren't simply going to accept their loss. Instead, they'll bring her back to life through alchemy.
The consequences of doing so are severe. Not only do they fail to resurrect their mother, they lose Edwards arm and leg, as well as Al's entire body in the process. They spend a long time mired in depression and regret but eventually resolve to move forward and figure out how to get their bodies back.
After Tenya Iida's older brother Tensei is assaulted by Stain, the normally rule-abiding hero-in-training is so furious that he decides to get revenge. This means breaking the law, since without a hero license he isn't allowed to go after criminals on his own.
He manages to track Stain down after taking an internship in the same city where he was last seen. The regret kicks in when he realizes how profoundly outmatched he is, and begins to think that he won't make it out of the confrontation alive.
In the end, Midoriya and Todoroki help him out, and they successfully defeat Stain. Iida still regrets his actions despite the positive outcome, because he was reckless and strayed from his core values.
One of the worst things that happens in the entirety of Code Geass happens because of an honest mistake. When Lelouch is explaining to Euphemia how his Geass worked, he accidentally activated it. Intending to give an example about the extreme things he could force another person to do, he accidentally ordered Euphemia to exterminate the Japanese race. With no willpower of her own to do otherwise, she started shooting at a group of people she had previously been fighting to protect and perished herself in the ensuing chaos.
While this wasn't exactly a conscious decision on Lelouch's part, he still chose to say the words aloud while knowing that his Geass was unstable. He couldn't possibly have regretted it more.
When you're the arrogant prince of Saiyans, sometimes you make decisions that aren't in your best interest because of your pride. That's what happens to Vegeta when he allows Cell to absorb Android 18 and achieve his final form, Perfect Cell. He could have stopped him from doing so, but he chose to allow Cell to grow more powerful after Cell taunts him for not challenging himself with powerful opponents.
Vegeta, Future Trunks, and Krillin are all taken out by Cell - a situation that could have been avoided if Vegeta just had a handle on his pride. Sure, Cell is eventually defeated and everyone recovers or is revived, but there was no reason to go through all that pain.