8bit pegged the winner. While not a movie per se, for the absolute best spy film ever you'll want to see the John Le Carré adaptations
Tinker, Tailor, Soldier, Spy (1979) and the follow-up
Smiley's People (1982).
Alec Guiness stars at quiet, retired spymaster George Smiley who has to uncover a mole in the British intelligence service, in a battle of the minds with his archnemesis Karla. These BBC mini-series get my vote for the absolute best television ever made, period, and easily the best spy fiction ever adapted for the screen, small, silver, or otherwise. Each runs about five and a half hours of tense, intricate cold war drama with absolutely no Bond-esque antics whatsoever. Alec Guinness is impressive in damn near anything, but he's positively amazing as Smiley. Both series are readily available on DVD and are highly, highly recommended.
Speaking of spy television, also be sure to check out at least the first season of
The Sandbaggers (1978-1980):
This 20 episode ITV series is another bit of gripping, realistic spy drama staring Roy Marsden as a complete and total bastard. If any of you have read the comic book Queen and Country, you'll recognize The Sandbaggers as it's direct inspiration. In any given 50 minute episode, at least 40 minutes are spent in offices researching, planning, and bickering between Marsden's character Neil Burnside and his staff and/or other governmental agencies. Or, as Burnside says in the first episode, "If you want James Bond, go to a library." The first season is astounding and features a clear storyarc to follow. The second season isn't quite as impressive (though still excellent) and the third, alas, a bit spotty. Don't let that stop you from checking out the first two box sets.
I also second the recommendation for The Conversation (which is easly Gene Hackman's finest moment and, quite possibly, Coppola's as well); it's not a spy film per se, but it does feature surveillance and paranoia as it's major themes. Astounding stuff. I'll also throw in a recommendation for Marathon Man (1976) (starring Dustin Hoffman
and Laurence Olivier), which has plenty of tension, more than a bit of paranoia, and some peripheral spy involvement. It also has a scene that will have you absolutely squirming in your chair. "Is it safe?"
FnordChan