ELIJAH : he decided that living with him was too dangerous for you, since you weren't supernatural and he wasn't willing to turn you. he believed that without him, you'd be better, so you two broke up.
KOL : you were startled when you found out about him being a vampire. you didn't feel safe or comfortable anymore, so you broke up with him. it was a sign of you not loving him enough, though.
JEREMY : you just drifted apart. neither of you were happy anymore, and you understood you both wanted to see other people so you just ended your relationship, thinking it was the best thing to do.
KLAUS : you weren't happy with his way to deal with things, how he was so obsessed with power and hurt people to get what he wanted. your love for him began fading, and you ended up breaking up because of it.
DAMON : he still had feelings for elena. he didn't cheat on you or anything, but you knew he and elena had unsolved things between them and it was too much for you to deal with so you broke up.
KAI : he hurt you too many times, with words and actions, and even though you tried to mend the broken relationship, he knew it could never be fixed. he broke up with you, knowing you deserved better.
STEFAN : you argued a lot, and your relationship turned from happy to unhealthy and bad. you both understood it quickly, and before things could get too serious, you broke up to avoid disaster.