Also was gonna post this. So... that's four. It's always worthwhile to note that new inductees of the Wire sometimes need three or four episodes to start to get into it. That was true of me, and I now consider in the best television series I've ever seen (and re-watched the whole thing at least three or four times).
Some good suggestion already. I'm not sure how literally to interpret your criteria so I separated them into categories. Here's my suggestions:
Gritty urban realism/working class struggles/crime/conflict with authority
Goodfellas (perhaps a bit violent?)
Gone Baby Gone
The Assassination of Jesse James by the Coward Robert Ford
In the Heat of the Night
Cool Hand Luke
In the Name of the Father
No Country for Old Men
Intense family conflict/existential issues/dark and tense inner struggles
There Will Be Blood
In My Father's Den
The Lives of Others*
The Hours (perhaps a bit depressing and heavy)
Who's Afraid of Virginia Woolf
The Night of the Hunter
* Kinda fit in both categories
INFP 4w5 so/sp
I've dreamt in my life dreams that have stayed with me ever after, and changed my ideas;
they've gone through and through me, like wine through water, and altered the colour of my mind.
- Emily Bronte
A man builds. A parasite asks 'Where is my share?'
A man creates. A parasite says, 'What will the neighbors think?'
A man invents. A parasite says, 'Watch out, or you might tread on the toes of God... '