Did George Lucas sanction that?!? 
I know The Godfather (and often its Part II sequel) gets a lot of love, but honestly I’ve never been able to make it through a viewing. It’s well filmed and acted and all that, but I just don’t find the characters interesting - I neither identify with them, nor find them so exceptionally evil (in a “Hitler documentaries on the History Channel” sense) that I care to delve deeper into their life stories. I find myself constantly asking myself, “why am I watching this again, except that everybody seems to love this?”
Plus, as Peter Griffin observed, “It insists upon itself”. 
I was only a child in the 1970s, but what movies have made a deep personal impact on me would be Star Wars, Jaws and Close Encounters of the Third Kind. And indeed, Enter The Dragon. Also Animal House, Grease and Saturday Night Fever. In a “that was an amazing movie” sense that I only appreciated as I got older, I would vote for One Flew Over The Cuckoo’s Nest and Rocky.
Though only Star Wars can claim the ultimate 1970s claim to fame: a disco version of the soundtrack’s movie theme.
Dang it, beat to the disco link due to a meeting at work intervening between the start and end of my post! 
That Coppola film. You know, the one with Marlon Brando and Robert Duvall.
*
Apocalypse Now.*
Rocky.
Loved it then. Saw it recently. Fell in love all over again. Exciting, moving, dynamic characters and acting. Underdog didn’t win … well, in a way he really did.
It’s almost like a parallel universe Stallone is in it. he seems so different from all the Stallone that followed.
Good decade for movies, lots of classics in there. The Godfather may be the best movie ever made, not just of the 70’s. Plenty of worthy runner ups.
I’m surprised Alien hasn’t been nominated yet. Perhaps because, as a 1979 film, it’s easy to imagine it was actually released in the 80s. But it’s a fantastic film - well-written, skillfully acted, and it produced a vision of the future as a lived-in place where blue-collar people work hard and die horribly that influenced pretty much everything that came after. Plus, it had Sigourney Weaver! And a kitty!
Dirty Harry.
I gotta agree. Star Wars was like nothing we had ever seen before. That opening scene still gives me shivers.
Just to mention a site with a big list of 70’s movies to look over:
Apocalypse Now or The Exorcist.
and still one of my all time favourite films All The President’s Men
I think Redford and Hoffman were well cast in the two main roles, but loved Jason Robards as Ben Bradlee.
Holy crap! I had no memory of that movie being that old! Damn I’m getting old!
I could never pick a single favorite, but I would consider putting Papillon in my top ten of the seventies.
Of the ones I saw (my parents took me to) during the '70’s:
Apocalypse Now
A Clockwork Orange
The Godfather
Alien
Jaws
Star Wars
…
Although I could repeat many of the great selling points of these movies as many have already mentioned, but I think I’ll have to go with…
…
A Clockwork Orange. I think seeing this at such a young age has jaded me forever upon movie violence. I still don’t see what’s so bad about it. I mean, I know rape/murder/assault is bad, but it’s not like Saw or Hostel or anything.
But this simply opened the door for Halloween (1978). All bets are off after that.
Also: Jaws made me afraid to swim in the pool.
The Conversation.
Well since my usual answer to, “What is your all-time favorite movie,” is generally Terrence Malick’s Badlands from 1973, I guess I should mention it.
More short-list additions…
Harold & Maude
Lone Wolf and Cub
Monty Python and the Holy Grail
Rocky
Animal House