Please note these are my ranking only of films I've seen. Any films you think should be on this list may be due to the fact I've yet to watch them. I welcome any recommendations of films which should be included.
My Neighbor Totoro
Stand and Deliver
The Thin Blue Line
Honorable Mention - The Adventures of Baron Munchausen, Bat 21, Big, Colors, Coming to America, Dangerous Liaisons, Dirty Rotten Scoundrels, A Fish Called Wanda, Frantic, Gorillas in the Mist, The Naked Gun, Powaqqatsi, Tapeheads, Who Framed Roger Rabbit, Women on the Verge of a Nervous Breakdown, Working Girl
Noteworthy films I haven't seen yet - The Accused, Akira, Another Woman, The Bear, The Big Blue, Drowning by Numbers, Eight Men Out, Grave of the Fireflies, Hairspray, The Last Temptation of Christ, Running on Empty, Time of the Gypsies, U2: Rattle and Hum, The Unbearable Lightness of Being
Films I think are overrated: Beetle Juice, Dead Ringers