I'm glad I found this thread. Almost all of mine (if not all) are room coms and I wanted to branch out. Glad you posted sleepninja
Let me tell you that the drama I just finished an hour ago was the MOST dramatic and had some of the MOST psychotic characters and was an actual emotional rollercoaster.

Kleun Cheewit http://mydramalist.com/13865-kleun-cheewit
I also recommend
Leh Ratree http://mydramalist.com/13397-leh-ratree

When you say dramatic and crazy.. all i can think of are makjang type dramas. Thus i think you should check put
secret/secret Love
million stars falling from the sky
kleun cheewit
new tales of a gisaeng
go go princess

but for drama with dramatic/psychological characters try
Soul
white christmas
nloody maunday
love me if you dare
Duel
signal
cruel city
hello monster
liar game
There is also:
Daisho
Hokuto
Kam Pood Tee Hai Pai
@Table122000 Oooh, Sawan Biang and Le Jun Kai were pretty crazy! I did enjoy them though. :)
** Please watch Kill Me Heal Me **
I'd also recommend taking It's Ok That's Love off the back burner... 
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. 
@Linus  I'd second Love Me if You Dare too.  I just finished that about a week ago and its amazing.