I saw this question posed on a movie forum recently and gave it some thought. I'm sneaking in one extra.
The Wedding Banquet (dir: Ang Lee) is about a gay Taiwanese man who fakes a wedding to a woman with his partner to please his traditional Taiwanese parents who don't know he's gay. It's funny, poignant, and heartfelt.
This might just be my favorite Ang Lee film because he captures the Chinese parent-child relationship so well especially when there's that generation/cultural gap between the parents who live in the home country and the kids who move to the US. To some extent I think every Asian kid can relate to the relationship- how there are things you don't tell your parents because you don't think they'll get it (but they do or they'll try their very best to).
Another one of Ang Lee's earlier films that I really enjoy is Eat, Drink, Man, Woman, which is is about a former chef and his three daughters. Like the Wedding Banquet, it starts off with a light, comedic tone but reaches quite a different and more serious tone towards the end. Eat, Drink, Man, Woman is about growing up and moving on. It also features some really magnificent Chinese cooking. One of my favorite food sequences on film is below.
The Children's Hour. The Children's Hour is a haunting story about how a little girl ruins the lives of two of her female teachers (Audrey Hepburn and Shirley Maclaine) after she spreads a rumor about them. I was impressed by how progressive it was since it was made in the 1960s.
This one is definitely a downer but I do wish more people knew about this movie since the messages it conveys are so important. It also has fantastic performances from Hepburn and Maclain.
Marty (1955). Marty (Ernest Borgnine) is a very well-liked butcher in his town, but he can't seem to get a girlfriend. When he finally finds someone he really likes and gets along with, none of his friends or family approve of her.
This is another older, black and white movie. Marty holds a very special place in my heart because this was one of the first older movies that I really enjoyed and connected with. I remember catching it on Turner Classic Movies and just being really charmed by all of the characters and the lovely plot development.
The Science of Sleep (dir: Michel Gondry)- a very imaginative movie about an eccentric man (Gael García Bernal) who confuses his dreams with reality. The Science of Sleep is filled with beautiful, creative imagery- it's really beautiful what they do in this movie without CGI using cardboard, foam, and other basic art supplies At a deeper level, Science of Sleep draws you in because of how personal the movie feels.
The Manchurian Candidate (1962). Before it was the Denzel Washington thriller, The Manchurian Candidate was a really haunting and gripping thriller about conspiracies, brainwashing, and assassination