What is YOUR favorite OLD movie?

I'll limit "old" to movies before 1980, otherwise the list would get too big.

It's a Wonderful Life
The Ghost and Mrs. Muir
Rashomon
High Noon
Dial M for Murder
Rear Window
12 Angry Men
The Apartment
Dollars Trilogy
Red Beard
2001: A Space Odyssey
Dersu Uzala
Alien

The usual suspect ツ

So, aside from that definition of old...

For me, at least before the '80s, it's a pretty easy decision to name The Sting (1973).

I have to admit that I'm a Marx Brothers fan so the majority of their old movies.

Probably Gremlins 2: The New Batch, I watched that movie so many damn times

I recently watched Some like it hot (1959), my 1st Marilyn Monroe movie, and I really enjoyed it!
In these last days I watched Per un pugno di dollari (1964), Gremlins (1984) and Lisbon Story (1994), all of them from very good to great, so many memories.
I'll check some other MM movie soon and will start a cycle of Federico Fellini, on my radar I have 8 1/2, and Amarcord at least.
Ah, and I have that Kubrick collection box still untouched...

The Great Escape (1963) Steve McQueen is my all-time favorite actor.

40s: Casablanca
50s: Vertigo
60s: Rosemary's Baby
70s: Hausu
80s: Blade Runner
90s: Magnolia
2000: JSA: Joint Security Area

I think. I've barely watched any films from the 40s, and the relatively few 50s-70s films I've watched are all (well, maybe except Hausu, which is nevertheless my sentimental choice) consensus really-great-must-watch stuff, which makes it hard to pick since they've all been so high quality. Probably could've made room for some Kurosawa on there... S'hard!

The Sound of Music (1965)
Операция «Ы» и другие приключения Шурика (1965)
Бриллиантовая рука (1969)
Dāvana vientuļai sievietei (1973)
Uzbrukums slepenpolicijai (1974)
Mans draugs — nenopietns cilvēks (1975)
Rallijs (1978)
Stalker (1979)
Limuzīns Jāņu nakts krāsā (1981)
Forrest Gump (1994)

I do find it adorable how many here consider movies from the 80's and 90's as "old" ^^

If you mean really, REALLY old:
Casablanca (1942) - I only watched it once, but absolutely loved it.
Nosferatu (1922) - Gotta say, even if it's a silent movie, and the effects and cinematography are pretty antique, it's still gave me the creeps as very few horror movies did. Even more so, since I watched it around Christmas time, in a brightly lit and snuggly heated room... I still got chills lol
It's a Wonderful Life (1946) - Yeah, it's a little bit cheesy, and the best part of the movie happens in its last 10-15 minutes, but I think it's incredibly heartwarming and a true Christmas classic.
Metropolis (1927) - I don't have to say much about it, an epic sci fi classic that inspired almost a century of sci fi films, and its social commentary is relevant to this day. I watched a remastered version, with new arrangement of the lost original score and newly found scenes that were rediscovered and inserted back into the film.
King Kong (1933) - One of the most popular giant monster films ever, and very entertaining. The special effects are mindblowing for its time!

The Boondock Saints
Final Destination
Gone in 60 Seconds

My favorite is "The good The bad and The ugly"
the second place prize goes to : "12 angry man"

teenage mutant ninja turtles. go ninja, go ninja, go, go

20s - The Kid
30's - Modern Times - City Lights
40s - Citizen Kane - Fantasia
50s - The Day that the Earth Stood Still - War of the Worlds
60s - Dr. Strangelove
70s - Brutti sporchi e cattivi - Young Frankenstein
80s - Kagemusha - My Neighbor Totoro - Airplane! - El Arreglo
90s - The Shawshank Redemption - As Good as it gets - Princess Mononoke

Depends on what you call old movie. If not my favourite overall, but definitely in my top 3.
Lawrence of Arabia

If I have to pick one:

One Flew over the cuckoo's nest

vampire hunter d

My favorite old Horror movie has to be The Thing

Die Feuerzangenbowle (1944) :)

View attached image.

If 1999 counts as old, then the choice is simple: American Beauty. I love satire and I hate suburban culture, and despite the plastic bag scene being so far up its own rectum that it could see daylight, the rest of the philosophy in the movie is wonderful; even that scene has a better version in the ending monologue of the film. Perfect depiction of the American Nightmare.

Seriously though, pre-2000 as old? Let's go with pre-1980. Some of my favourite classics (all pretty obvious, I admit):

2001: A Space Odyssey, A Clockwork Orange
Rosemary's Baby
Picnic at Hanging Rock
Life of Brian, Monty Python and the Holy Grail
Turkish Delight
Last Tango in Paris
Solaris, Stalker, The Mirror
Apocalypse Now
Aguirre, the Wrath of God

My Top 3 favorites of all time seems to fit the description.

Goodfellas (1990)
The Good, the Bad and the Ugly (1966)
Beetlejuice (1988)

My favourite "old" movie is literally my favourite movie ever:
2001: A Space Odyssey

I do like My Fair Lady (https://www.imdb.com/title/tt0058385/).