35 sai no Koukousei - the female lead is a trouble-maker and she's kind of a rebel, while the male lead (the teacher) is, like you said, an upright, responsible guy
The Memorandum of Kyoko Okitegami - the girl forgets everything she's done within a day after she sleeps, so her situation is pretty problematic, and the guy is just a sweet, kind person, who always wants to help her
Tokyo DOGS - the girl has some problems and she's protected by two guys who even though they're kind of weird too, they're not bad people
Biblia Koshodou no Jiken Techou - the female lead is very strange and she's basically an introverted, while the male lead is more of an normal, level-headed guy
Otenki Onee-san - a weird girl and a pretty normal guy
Celeb to Binbo Taro - it's about a very rich girl with an arrogant attitude who changes her values after meeting a poor, but kind-hearted man
Take Care of the Young Lady - similar plot as the one before
Ohitorisama - the female lead is an workaholic and has her issues, while the male lead is a shy, but level-headed guy
Zenkai Girl - similar plot with the one above
Q10 - the girl is actually a robot and obviously, she has a werid behaviour and the guy is just a normal, but open-minded person