Okay, I am looking for a character that sincerely regrets teasing/cheating/raping/bullying/etc. I do not care if it is the tachi or the neko who is regretful, as long as it is a major part of the plot. I would especially like it if the other character is not forgiving, or at least doesn't forgive easily, so that the regret is even stronger. I don't want them to just feel bad about hurting the other person, I want them to feel completely tortured over it if at all possible. I read Doushitemo Furetakunai and Imadoki no Shishunki already, as well as a few others I've since forgotten, and would really like to see if there are any more which include this in the plot.

You might try these. Sorry, this is all I can think of.

Dolce, though more from the point of view of the victim. (rape)
Name of Love, maybe (cheating)

Sono Kuchibiru ni Yoru no Tsuyu

Thank you! I'm almost finished with these now, can anyone think of more?

Kyuuso wa Cheese no Yume o Miru
Ubawareru Koto Marugoto Zenbu

demian syndrome

Thanks for all of the suggestions! Is it possible that there are more? It doesn't have to have a happy ending or have the characters get back together, it doesn't even have to be the main couple as there was one I read in which it was a past relationship (one of the guys outed the other at work for some reason, so the outed one moved to a new company but the 'bully' was still in love and regretted what he did, I think...)

Anything similar is definitely welcome, as long as a simple apology (or worse, sex with no apology) isn't the fix-all.

I Shall Never Return 5 volums Great manga (but awful anime, never watch!)
Scarlet
These mangas suit your "sincerely regrets", but they don't for "the other character is not forgiving"...
Oh, just remembered: Jazz goes there too.