Images (Robert Altman)
A Woman Under the Influence (John Cassavetes)
Zabriezke Point
Diabolique
Pierrot le fou
The Wall
El (Him)- Bunuel
Psyche 59
Back in the 60s and 70s there were a lot of movies with characters going nuts. So many that a term was coined for them, “Psychological Films”.
There’s a pretty extensive list of these.
http://mubi.com/lists/hysterical-in-a-floral-dress
Let’s not forget Marie Antoinette.
Repulsion
THE VIRGIN SUICIDES
ba-da dum!
Well, if you want to go there:

2 of my favs. I stand alone and The tenant.
When I think about films with people going over the edge, “Falling Down” is easily my first choice. It’s so wonderfully captured, brave on all of the actors’ parts, and so sharply written with attention to detail to boot.
If you want to get current, two other great films on the subject are “Shame” and “Take Shelter.”
@Brian P
Thumbs up for recognizing MMMM.
Bergman immediately came to mind: Through a Glass Darkly, Cries and Whispers, Winter Light, A Passion For Anna, etc…
Others:
Pink Floyd: The Wall (not a great or even that good of a movie, but some seriously great animated sequences are here that will make you lose your shit)
Chronicle
I Saw The Devil
Antichrist
Melancholia
Super
The Lost Weekend
Platoon
Falling Down
One Flew Over the Cuckoo’s Nest
How can there be a thread on this topic and not one person has yet mentioned Taxi Driver, the greatest “losing it” film of all time?
Some others:
Leaving Las Vegas
Dead Ringers
Walking Tall
Affliction
Birdy
Casualties of War
For some reason I thought of comedies. I guess, I enjoy seeing people get really exasperated. Two films that come to mind:
Blind Date with Bruce Willis and Kim Basinger. This isn’t a great movie, but Willis, a mild-mannered musician, I enjoyed him “lose it” from a very frustrating date.
I enjoyed Nicholas Cage in Honeymoon in Vegas for similar reasons.
Network
Surprised at no mention of Cronenberg’s Naked Lunch or Spider. Even Videodrome can be seen as a study on mental breakdown.
First Blood
A Bittersweet Life
I like;
Who’s Afraid of Virginia Woolf?
The Pumpkin Eater
A Face in the Crowd
The King of Comedy
Edward the Bonobo
Films about people losing it. The spiral of despair and all that. Not The 40 Year Old Virgin
Apocalypse Now.
The Shining.
Shallow Grave.
Falling Down.
Clockwise
After Hours
Death in Venice.
…More?