Great thread! But I have to disagree on these movies being timeless experiences, because the way people perceive movies has changed a lot.
For example: Rear Window by Alfred Hitchcock - shocked people in the 50s, leaves you rather unimpressed today, because as time went by, filmmakers were constantly pushing the boundaries of this genre.
Another example: Annie Hall by Woody Allen - has an average shot length of 14.5 seconds. Then MTV came up with music videos and today we have shot lengths that are significantly shorter. The pace of the narrative is faster in general. So, as we’re used to movies being told faster than those made in the 70s or earlier, we could get bored by narratives and shots that now seem unusually long.
Nevertheless, among these classics there are of course some, that I would consider timeless, but surely not all of them.
Now back on topic: I’ll start in the early days. And because I’m German, the first two movies I recommend are of the German expressionism period.
The Cabinet of Dr. Caligari (1920) – a silent horror film by Robert Wiene. This movie has influcenced recent works of Terry Gilliam (The Imaginarium of Dr. Parnassus) and Martin Scorsese (Shutter Island). However, it left its biggest impression on director Tim Burton, whose visual style is an extension of what you can see in this movie.
http://www.youtube.com/movie?v=ALqnSUMHPrA&ob=av4n
Metropolis (1927) – a movie by Fritz Lang. This movie is probably the first great sci-fi movie and the role model for Cyberpunk and movies like Blade Runner.