My top pick is probably different from post people's, but I really like this dystopian viewpoint and if you go back and watch it again you'll find that it hits the mark as well as Aldus Huxley did with Brave New World. The rest of my picks you'll probably agree with, but lets hear it.

Rollerball (1975) -- James Caan, John Houseman http://en.wikipedia.org/wiki/Rollerball_(1975_film)

Rollerball is a 1975 science fiction film directed by Norman Jewison from the 1973 short story "The Roller Ball Murders" by William Harrison, which was published in Esquire magazine and subsequently nominated for the Pulitzer Prize. Harrison himself wrote the screenplay for the film.

Logan's Run (1967) http://en.wikipedia.org/wiki/Logan%27s_Run

Logan's Run is a novel by William F. Nolan and George Clayton Johnson. Published in 1967, it depicts a dystopian future society in which population and the consumption of resources is managed and maintained in equilibrium by the simple expediency of demanding the death of everyone upon reaching a particular age, thus neatly and inhumanely avoiding the issue of overpopulation which was of growing concern at the time. The story follows the actions of Logan, a Deep Sleep Operative or "Sandman" charged with enforcing the rule, as he "runs" from society's lethal demand.

Fantastic Voyage (1966) http://en.wikipedia.org/wiki/Fantastic_Voyage

The United States and the Soviet Union have both developed technology that allows matter to be miniaturized using a process that shrinks individual atoms, but its value is limited because objects shrunk return to normal size after a period of time - the smaller an object is made, the quicker it reverts. Scientist Jan Benes, working behind the Iron Curtain, has figured out how to make the shrinking process work indefinitely. With the help of the CIA, he escapes to the West, but an attempted assassination leaves him comatose, with a blood clot in his brain. To save his life, Charles Grant (the agent who extracted him, played by Stephen Boyd), pilot Captain Bill Owens (William Redfield), Dr. Michaels (Donald Pleasence), surgeon Dr. Peter Duval (Arthur Kennedy) and his assistant Cora Peterson (Raquel Welch) board a submarine, the Proteus, which is then miniaturized and injected into Benes. The ship is reduced to one micrometre in length, giving the team only one hour to repair the clot; after that, the submarine will begin to revert to its normal size and become large enough for Benes' immune system to detect and attack.

Soylent Green (1973) http://en.wikipedia.org/wiki/Soylent_green

Set in the year 2022, Soylent Green depicts a dystopia, a Malthusian catastrophe that occurs because humanity has failed to pursue sustainable development and has not halted uncontrolled population growth; New York City's population is 40,000,000, with more than half of it unemployed. Global warming, air and water pollution have produced a year-round heatwave and a thin, yellow, daytime smog. Food and fuel are scarce resources because of animal and plant decimation, housing is dilapidated and overcrowded, and widespread government-sponsored euthanasia is encouraged to control and reduce overpopulation. Meat, bread, cheese, fruit, vegetables, and even alcoholic beverages are scarce and extremely expensive; for example, a six-ounce jar of strawberry jam is 150 "Ds" (US Dollars). Like the soylent food factories, the farms producing foodstuffs are heavily guarded and off-limits to civilians. For most of the populace, natural foods are a rarely, if ever, enjoyed luxury. The government dispenses rations of synthetic food — soylent yellow, soylent red — made by the Soylent Corporation; their newest and most popular version, soylent green, is made from plankton, according to the food firm.

Andromeda Strain (1969) http://en.wikipedia.org/wiki/Andromeda_strain

The Andromeda Strain (1969) is a techno-thriller novel by Michael Crichton. The plot concerns a team of scientists investigating a deadly disease of extraterrestrial origin which causes rapid, fatal clotting of the blood. This novel established Crichton as a best-selling author.

After that, there are a host of others:

2001: A Space Odyssey
Planet of the Apes
The Day the Earth Stood Still
Forbidden Planet
Damnation Alley
A Boy and His Dog
Invasion of the Body Snatchers
Parts: The Clonus Horror
The Island of Dr. Moreau
The Iron Giant

There are some great ones that are too recent for me to put on my classics list, but will be classics

The Matrix
Blade Runner
Alien
Aliens
Outland
The Fifth Element
Star Wars
The Road Warrior
The Empire Strikes Back
Star Trek II - The Wrath of Khan
Enemy Mine
The Last Starfighter

On the less serious, but more fun side:

Dark Star
Buckaroo Banzai: Across the Eighth Dimension
Attack of the Killer Tomatoes

Ok, your turn. What obvious top picks am I missing?