Ill write down a few movies, that have left a lasting impression on me. Also four of them have already appeared in that thread but without any comment or description.
Life in a fishbowl - pretty good icelandic drama, details the lives of several loosely connected people. reminded me of la crash.
Notre petite soeur - drama/comedy about three japanese sisters.
Short term 12 - was one of my favourites the year it got released. Brie Larsons breakthrough - you probably know that one since "Room", the next movie with her as a lead got more than enough media coverage. basically shes a caretaker in a facility for abused kids but also wrestles with her own demons. This one got mentioned before but since you didn't quote it, its possible you havent watched it yet - if not, do it!
la vie d'adele/the warmest colour is blue - yep, theres an unessecarily long lesbian sex scene in it but its much more about their relationship, any relationship really. great acting
The virgin suicides - already got posted, sofia coppolas debut and my favourite of her, a group of boys connect with four (i think) mysterious sisters. this one got a dreamlike, nostalgic quality, which i really liked
After sunrise/sunset/midnight - my favourite romantic movies, not a romcom - much talking, bit of drama in between but great acting and writing. if you're not at all into romance - skip them
Mr Nobody - impressed me a lot when i was younger. Deals with alternative realities but ponders more to emotions than its theoretical frame work for which if you will can judge it, still a great experience.
Man bites dog/C'est arrivé près de chez vous - camera crew follows a serial killer. feels nouvelle vague, black comedy extreme
Last year at Marienbad - i only recently got around watching it. a man and a woman meet at a spa and rekindle their real or imagined relationship. Shot in black and white, with countless shots of the hotels interior, long winded descriptions of it and hotel guests, that quite figuratively serve as background it is not easy to watch and you arent left with a definitive explanation. If you like movies, that constantly challenge you to figure out whats going on and have the patience to immerse yourself into one where not much is actually happening - this one might be for you.
Green Room - already got posted. just a really well done, gritty action movie. punk band somehow ends up playing for neo nazis and have to fight for more than their pay
The Crow - my favourite super hero movie. classic revenge story set in a dystopian hells kitchen with lots of gothic flair - yeknow tomb stones, ravens, rain, leather clothing.. also the lead actor (son of bruce lee) got accidentally killed at the set, guess that also helped turning it into a cult film
Hero - one man tried to assassinate the emperor, now different swordmen are interrogated and must tell the story of what happened - each of those is shown in a different colour scheme fitting what is told and reveals new facts. best jet li, best wuxia period, no probably not but im biased - on of the first movies i watched in cinema
Ghost Dog - hip hop culture plus lonesome samurai hitman. must watch. after that check out the rest of jim jarmuschs filmography, "dead man" is also great
Le Samourai - great film noir with alain delon aka coolness personified
Upstream Colour - you might have watched it, its from the same director as Primer. Relies heaviliy on visual metaphors to tell its story and same as with Primer I had absolutely no idea what had happened after the first watch^^
Spring Breakers - yeah, that one isnt nearly as "critically acclaimed" as most on the list are. Three innocent teen girls (unfortunately including the insufferable Selena Gomez, fortunately she doesnt get much screen time) go to Mexico over Spring Break and get mixed up with a local drug dealer, who feels he has found his soul mates. You can read it as social commentary, judge it as an attempt by an aging director (Harmony Korine, Kids) trying to be relevant again or just enjoy the visual force and surreal scenes it packs.
Enter the Void - follows the routine of a drug dealer in tokyo through his eyes = pov to the extreme,
Hunt for the Wilder People - new-zealandian comedy about a foster boy on the run from authorities. Extremely funny, if you liked it check out "What we do in the shadows" - mockumentary about vampire room mates by the same director.
The Lobster - plays in a dystopian community where people if they dont find a partner after a certain age get turned into animals. Yep, thats exactly as wtf as it sounds. It is funny but the humour is as dry and subtle as it can be.
Nocturnal Animals - one of the newer entries. dunno if its favourite movie material but an intelligent, well crafted thriller with great visuals. somehow left an impression. sbd described it as "this years gone girl" which i think is fitting
Neon Demon - same director as Drive (Nicolas Reyf something), so probably on your radar. Ill be honest and say, that its purely in here because the visuals and the cinematography were impressive. I kinda liked, how superficial and obvious it seemed in its symbols and metaphors which together with the whole model theme felt fitting and also as a big fu to over analyzing movies as well as the obsession of being "deep" and "meaningful". Yeah i know, very ironic^^
The Mermaid - big budget chinese retelling of the mermaid with critical undertones regarding water pollution/ecological issues. As usual in chinese comedy the comedy is extremely over acted and exaggerated. Huge part of its enjoyment for me was the strange mix of drama/over the top comedy and serious action. Directed by Stephen Chow whom you might know from Kung Fu Hustle. - even better movie, watch that one first
99 Francs - imagine fear and loathing in las vegas with marketing executives in france, i dont think i have to mention drugs
Chronicle - coming of age with super powers in blair witch found footage style. by no means a master piece but i liked the realistic look of it, also there arent suddenly a crime syndicate and a love interest appearing like in Kick-Ass
YiYi - daily life of three generations of a taiwanese family - cant write much about, it was just good
A Scanner Darkly - undercover narcotics agent gets addicted, trippy visuals and some nice twists
Natural Born Killers - about two serial killers and the fascination of the media with them
The Artist - won a few oscars, you probably know it. Black and white movie about the transition from silent movie to sound, plays cleverly with both.
thats what i can think of the top of my head. you dont seem nearly as much into drama as me, so just skip them^^ should still be more than enough recommendations.