Your first movie is 7 Days in May and your second movie is The Bedford Incident.
Enigma(1983) is a superb cold-war spy thriller. Warning, there are a bunch of other films with this same title. This one is a UK/French production starring Martin Sheen. It’s not yet available on VHS or DVD, unless you’re in Germany.
No Way Out with Kevin Costner is a murder mystery set in the context of the Cold War.
Here’s a couple more examples of intelligent British cold-war drama that aren’t available in the USA (OK, I’m whining.)
Game, Set and Match television series, based on Len Deghton’s first trilogy about Benard Samson.
http://us.imdb.com/title/tt0092360/
Smiley’s People (1982) which is a British mini-series based on one of my favorite Le Carre novels.
http://us.imdb.com/title/tt0083480/
On the bright side, The Russians are Coming, the Russians are Coming (1966) is a wonderful light comedy that was released on DVD earlier this year.
Darn. WereOtter beat me to The Russians are Coming, the Russians are Coming. Okay, I’ll mention SPYS* instead - Elliott Gould, Donald Sutherland, and a bunch of asterisks attempt to repeat the success of MASH* with a cold war comedy.
How about two Gregory Peck classics? The Chairman and On the Beach. Although I guess the later could be considered a post-Cold War movie.
Isee Little Nemo beat me to On the Beach 
How about The Hunt for Red October ?
or a HBO movie, By Dawn’s Early Light or a weird one, Ladybug Ladybug ?
Threads and The Day After were both post-nuclear armageddon movies.
Strategic Air Command, with I believe Rock Hudson (or maybe Jimmy Stewart? I think Rock Hudson was in a SAC movie as well).
Just checked… Strategic Air Command did star Jimmy Stewart. Rock Hudson was in another SAC movie called A Gathering of Eagles.
Speaking of Rock Hudson - he was in another cold war movie called Ice Station Zebra.
Another one not mentioned is The Right Stuff, which is definitely a cold war movie. And a great, great film. One of my favorites.
Iron Eagle! And Iron Eagle 2! And um…the third one…um…
(You wanted cheesy 80’s Cold War movies that there never should have been sequels to, right?
Wow, thanks for the suggestions everyone. It’s gonna be a busy movie-watching weekend.
(err, I’ll have to think about Iron Eagle, though :D).
Thanks Detop.
Both those shows were good, IMO.
Matinee. (Really!)
The Spy Who Came In From the Cold.
One, Two, Three, an unusual Cold War comedy by Billy Wilder, starring James Cagney.
Invasion of the Body Snatchers (original version)
They’re not movies, but the Twilight Zone episodes “The Monsters Are Due on Maple Street” and “The Shelter” are prime slices of the Cold War.
I’ll go along with the recommendations of…
The Manchurian Candidate
The Spy Who Came in From the Cold
and
On The Beach
And I’ll add…
Atomic Cafe
The President’s Analyst
and
The Third Man
Yes! A very underrated movie. (I’d love to see a full-length version of Mant)
Did anybody mention Seven Days in May? Cool flick, very tense.
John Frankenheimer was one of the best.
The Beast starring George Dzundza and Jason Patric (1988). A good movie about a tank crew during Russian war with Afghanistan.
also
Spies Like Us. 
“The President’s Analyst!”
That is one groovy far-out movie!
The President is cracking up under pressure of the job, and so James Coburn is hired to be his analyst. But for security reasons, Coburn cant get his own head shrunk. so he cracks up and goes AWOL. Of course, all the secret services of the world - and other powerful organisations too - are on his trail, hoping to capture him and find out all the deepest governmental and presidential secrets. The sort of comic caper that Austin Powers aims for and missed.
The James Bond series is certainly Cold War, except for the last one or two.
The Day After was a made-for-TV film, but hey…
I’ve always enjoyed Firefox.
I managed to watch two recommended movies this weekend: Thirteen Days and The Manchurian Candidate (they were the first two that I could find).
(Possible spoilers - no boxes)
Thirteen Days: Pretty decent movie, actually. I thought it told the story pretty well. I guess my only problems with it were: it’s half-an-hour too long; the random transitions between black and white and colour near the beginning. What was that for?; Costner trying to pull off the JFK accent (thanks for the warning, Kaspar 
); and the amount of screentime that Costner’s character gets… I thought the film could’ve done just fine without him.
The Manchurian Candidate: Wow… just wow. One of the best thrillers I’ve seen. The dream sequences were amazing, the acting was great (the first film of Sinatra that I watched) and the script impressive. I didn’t get the “are you Arabic?” dialogue on the train, though. I’ll be watching this one again, no doubt.
Thanks again.