Great thread. I have so many favorites, but I usually can't think of them when I try to post lists. These are the ones I own on DVD so I guess they are my favorites --
You didn't ask for the 1920s, but I'm a big fan of some silent films, and I think a handful should be listed here....
1920s:
Safety Last (1923) Directed by Fred C. Newmeyer & Sam Taylor) starring Harold Lloyd
The Gold Rush (1925) Directed by Charlie Chaplin

I fell so in love with Chaplin films, I wanted to get a film poster (a repro
of course) and although my favorite of his was City Lights (coming up next decade), I opted for this one -- image above, as I liked the poster art more a lot more. This is great fun, and if you haven't watched a Chaplin movie, you definitely should, whether it's this one or one of the ones coming up in the 1930's section.
1930's
City Lights (1931) Directed by Charlie Chaplin

In my top 10 films of all time. A true masterpiece and essential viewing by anyone who considers themselves a true cinema fan.
Modern Times (1936) Directed by Charlie Chaplin

This was considered Modern Times back in 1936. Sadly enough, the relevance to the U.S. working conditions right now have often reminded me of this film.
It Happened One Night (1934) Directed by Frank Capra

I sought this one out after reading that
Bronco Billy was more-or-less a modern retelling of the movie (or if my memory isn't good, at least it was compared to
It Happened One Night) and it is a great comedy, so much fun.
Mr. Smith Goes to Washington (1939) Directed by Frank Capra

Also in my Top 10 films of all time -- maybe in the Top 3.
M (1931) Directed by Fritz Lang

Another film that is a must-see for cinephiles.
The next two star James Cagney.
Angels with Dirty Faces (1938) Directed by Michael Curtiz

Another that might break into my Top 10 of all time. My favorite Cagney film.
The Public Enemy (1931) directed by William A. Wellman

The grapefruit scene -- hilarious. But this movie is inherently rewatchable.
The 1940's
So many great films in this decade, I'm sure I'll leave out a lot of them.
Casablanca (1942) Directed by Michael Curtiz

Perhaps the most beloved classic film of all time... and one of my favorites, as well.
Citizen Kane (1941) Directed by Orson Welles

This is one of those films that you can take almost any screencap from it and you'd have a piece of art, worth of framing and hanging on your wall. Give it a shot if you don't believe me. Plus, the story and acting are perfect.
The Great Dictator (1940) Directed by Charlie Chaplin

Strong message and amazing this was released in 1940 and not 15 or more years later.
White Heat (1949) Directed by Raoul Walsh

Another great Cagney movie, and here's one more for good measure....
Yankee Doodle Dandy (1942) Directed by Michael Curtiz

Anyone who loves Cagney's gangster films needs to watch this one to get a true appreciation of his wide range of talent.
The Third Man (1949) Directed by Carol Reed

Fabulous film-noir starring Orson Welles.
The Philadelphia Story (1940) Directed by George Cukor

The penultimate comedy romance with Katharine Hepburn at her most stunning.
It's a Wonderful Life (1946) Directed by Frank Capra

Great at Christmas, but equally enjoyable all year round. This is probably the film that made me a James Stewart fan, he's fantastic here.
Rebecca (1940) Directed by Alfred Hitchcock

One of my Top 5 Hitchcock films, and looking over his filmography, this is the first one he made that I truly loved.
And since we're in my favorite decade of Hitchcock films, here's two more which he released back-to-back
Spellbound (1945) Directed by Alfred Hitchcock
Notorious (1946) Directed by Alfred Hitchcock

There's something so creepy about that staircase with the black/white tile floor that it's the image that is cast in my mind whenever I think of this film, similar to Kubrick's shot of the twins in the hotel hallway in
The Shining. Anyway, this is a great film, and one of my favorite Hitch films.
The Big Sleep (1946) Directed by Howard Hawks

Lauren Bacall is transfixing - try peeling your eyes off the screen when she's on it.
The Maltese Falcon (1941) Directed by John Huston

Another great Bogart film of many this decade.
Double Indemnity (1944) Directed by Billy Wilder

Barbara Stanwyck's best, in my opinion. One of the greatest in the film-noir genre.
That's already a lot for the 1940's, and while I'm sure I'll kick myself for missing something spectacular, I'll move on now to ...
The 1950's.
Sunset Blvd. (1950) Directed by Billy Wilder

Another from my Top 10. About 5 years ago, I had my entire nuclear family staying with me for a week. Trying to keep everyone entertained, I put on some great movies with broad appeal, starting with
City Lights, and then the next night, this one. In my mind, no one could possibly dislike this movie. More than an hour into it, my brother asks "Don't you have any current movies we can watch?" I was shocked "You're not enjoying this?" My father responds "Not at all." And it was that moment that I was reminded that I, for whatever reason, had little to nothing in common with any person in my family. I made them finish it, thinking by the end scene, it would win them over. My brother asked "Were you really expecting us to like this piece of crap?" So, at this point, I wonder how I'm going to get through the rest of the week. Maybe time to put on
Titanic. Anyway,
Sunset Blvd. is a classic that EVERYONE will love unless they're a member of my family.
Strangers on a Train (1951) Directed by Alfred Hitchcock

Another great must-see Hitchcock film.
Touch of Evil (1958) Directed by Orson Welles

Another classic film-noir that stars one of my favorite actors (and directors) Orson Welles.
And here's five from one of the best directors of all time:
The Wrong Man (1956) Directed by Alfred Hitchcock

Another of the best Hitch films, starring Henry Fonda.
Rear Window (1954) Directed by Alfred Hitchcock

I can't imagine there's anyone here who hasn't seen this movie, but if you haven't, put it on your watchlist asap.
Dial M For Murder (1954) Directed by Alfred Hitchcock

Another directed by Hitch starring Grace Kelly. Need I say more?
Vertigo (1958) Directed by Alfred Hitchcock
North by Northwest (1959) Directed by Alfred Hitchcock

Gentlemen Prefer Blondes (1953) Directed by Howard Hawks

Marilyn was the ultimate screen goddess, and in my opinion, was never more stunning than in this film.
And again, I'm sure I'm missing a lot, but moving on to....
The 1960's
A Hard Day's Night (1964) directed by Richard Lester

So real, it's almost nonfiction. The dawn of Beatlemania in America captured on film, and a witty screenplay as well. The four individual personalities of The Beatles are created, and will hold for the rest of their lives.
(Won't add the spaghetti westerns here, everyone knows they belong on this list, and we've all seen them).
Once Upon a Time in the West (1968) Directed by Sergio Leone

A Leone masterpiece.
Rosemary's Baby (1968) Directed by Roman Polanski

One of the finest horror films of all time. Creepy as hell.
Three more from Hitchcock:
Psycho (1960) Directed by Alfred Hitchcock
The Birds (1963) Directed by Alfred Hitchcock

I absolutely love the scene where the birds start out with just one or two on the wire, and then a few more fly in, and then when the camera comes back, a few more, and then... my blood ran cold the first time I saw all those birds lined up. It still has a strong effect, though after multiple viewings, a little less.
Marnie (1964) Directed by Alfred Hitchcock

Sean Connery directed by Hitchcock! For a while, this was my favorite Hitch film.
The Apartment (1960) Directed by Billy Wilder

Sensitive and sweet comedy that has a sad undertone. Great acting by Lemmon and MacLaine.
Enough for now.
