Second Kill Me, Heal Me, W and Love me if you dare. I wonder if Another Miss Oh wouldn't kind of fit into this description, too. He's not necessarily psychotic, but... the main character has some quite unique characteristics and has to see a psychiatrist, too.
There are some dramas that have dramatic story lines, but don't have psychotic characters in them. I would say You're All Surrounded is like that. Also, I am currently watching the Hospital Ship and the amount of drama in this show has been pretty high so far.