Hate:
Sherlock (the TV series)
Fight Club
Benny and June
Shutter Island
Me, Myself and Irene
13 reasons why
The virgin suicides
American psycho
One flew over the cuckoo's nest (mcmurphy was in jail for statutory rape, hardly a lovable rogue)
Any Horror or thriller with a twist that makes the lead character or villain have D.I.D/multiple personalities, which most people mistake as Schizophrenia.

Like:
Perks of being a wallflower
Black Swan
Donnie Darko
It's kind of a funny story
Girl, interrupted
Bug
Eternal sunshine of the spotless mind
Primal Fear
Homeland

N. B. I'm not basing my opinion on how realistic I believe the shows or films to be but on where I think there is a good balance between entertainment and not wrongly romanticizing or undermining those with mental health issues.