Hey,
I am listening this old dixieland and New Orleans jazz compilation,
wondering are there many games with just even one tune of old music,
and by old music meaning the stuff before like mid-1950's or so.

Like I know it's a tough call to ask for a game to have all of its soundtrack be,
say Dixieland or Delta Blues or such... But are there any games with just
at least a song or two, or a few?

They just bring this nice relaxed vibe to me sometimes, it's hard to describe.
I remember Grim Fandango had some great old tunes, and the whole game
is great, but I've been in the Land of The Dead quite enough :D

While I don't think any of the songs are as old as you are looking for the closest I can think of off the top of my head to what you are asking is Fallout 3 and Fallout 4 with their radio stations

The FPS Fallouts and Mafia (atleast 1 and 2).

A Golden Wake

https://youtu.be/Q0I_3KcPKKY?si=y8B8BXYUHQat522F

Cuphead

https://youtu.be/ReVgL5sSUhc?si=66J_eYn9bimaZetA

Stick it to the Man

https://youtu.be/ldgElQW7RU0?t=62

Sam & Max Series

https://youtu.be/BhuiWcqcLGE?si=VxevUPcZ7ZhWJKWd

Evil Genius

https://youtu.be/jE9j8jnX0WY?t=118

Ever since i listened to this epic Techno track in Vampire Coteries
https://www.youtube.com/watch?v=8aCGnb5v0cw
I literally can't think of anything else to say whenever this question 'bout music and games pops up. Maybe you like it too :-)

While it's OST is not "old", as in: "recorded in the 1950s or earlier", it's definitely jazzy:

- Blacksad: Under the Skin: https://www.gog.com/en/game/blacksad_under_the_skin

And it's been a while since I played it, but I think I remember hearing old blues/jazz songs being played in Mafia III: https://www.gog.com/en/game/mafia_iii_definitive_edition
Though I'd guess, those were rather from the 1960s (given the time, the game's set in).

The Saboteur has some music that old.

https://www.gog.com/en/game/cuphead comes to mind.

- Bioshock 1-3.
- Fallout 3, NV & 4.
- Lemmings
- Maid of Sker
- The Saboteur

Edit: If you mean in the style of say old jazz, etc, there's a lot more (eg, 1954 Alcatraz, Contrast, Grim Fandango, No One Lives Forever, Sam & Max series, etc), vs specifically limited to just actual old 1900-1950 songs. Technically any pre-1950's tune will also include a lot of classical music.

OpenTTD has several music selections over several genres, including the original TTD & new jazz renditions. Course, that one is MIDI, so you'll want a good soundfont.

Any Aminita Productions game will have the work of DVA in it, who while not jazz, produce very unique music.

SimCity 3000 is a free jazz album that comes with a game; Jerry Martin & the EA orchestra were at their peak output here.

SimCity 2000 might count too but the music is much more moody and dark. Plus it has to be interpreted.

Locomotion, being the lesser regarded sequel to Transport Tycoon, also has much the new selection of music, including a bit of jazz for starting in the 1900s.

Railroad Tycoon 2 & 3 (the original didn't have much music), and SMR have bluegrass, which certainly is a Jazz Adjacent.

Sam & Max and The Duck Detective, being a lampooning and parody of Noir detective stories respectively do reflect this in their musical selections. Sort of.

Earthbound's music may seem simplistic, but the general beats and style tend to hew towards jazzlike tunes that have their own beat to them. (Battle Against an Unsettling Foe) Some tracks in Super Castlevania IV mix with this, chamber music, and horror too.
[url=https://modarchive.org/index.php?request=view_genres]
The veritable ModArchive has over 200 selections of Jazz labled music.[/url] Though if any of it meets your standards would remain to be seen and would require something beyond a basic player as most of that is in tracker music formats.

Oh, thank you very much for everyone!

There is a lot of this kind of music, wonderful to hear!
Amanita games, Blacksad, Duck Detective etc. sound cool :)

These days mostly playing slow-paced games, like point'n'clicks and turn-based rpgs,
happy to hear there this music exists as well.
Sounds like end of summer game purchase(s) coming up :)

I was eyeing (or rather trying to prick my ears to) Thaumaturge and it seemed to have
some sort of fusion of old and more modern...
Maybe Railroad Tycoon 2 could be nice to check - big fan of trains : Sunless Skies is currently a main go-to :)

Cheers everyone!

Ps. Keep going if there's more :D