There are a lot of musical pieces out there in the public domain that are immediately recognizeable and potentially good for games. I'd like to start a list here.
Please note, though, that just because a musical score is public domain, it doesn't follow that a recording of that music is public domain. In fact, if you find recordings of any of these works around the web, you should assume that they are not public domain unless otherwise specified.
To find public domain music scores, I recommend the IMSLP (International Music Score Library Project) website, which contains many original musical scores and arrangements of those scores, along with licensing information. DO NOT ASSUME THAT ALL WORK ON THE IMSLP IS PUBLIC DOMAIN. The licenses are listed with the musical scores, and some scores are available under other licenses. Note that any recording of a musical arrangement is a derivative work of that arrangement, so if you find an arrangement that's licensed CC-BY-SA, then your recording of it must also be CC-BY-SA.
Finally, note that the recordings that I'm linking to as examples are not public domain.
So, to get started:
I'll probably look around more later, but for now I'll pass it off and see if other people can find some stuff.
As for ways you can use this music in your games, be creative! The familiarity of these songs makes them excellent for use in arrangements, sometimes to great dramatic or humorous effect.
Finally, note that OpenGameArt is based in the United States and follows US copyright law. At least one of the above pieces is not public domain in Europe, so please be aware of the implications of copyright law in your country before using these pieces.
Faure's Sicilienne would be amazing overworld music for an RPG: https://www.youtube.com/watch?v=U5Y0uQLgriA (this recording obviously not PD)
Pavane, also by Faure, probably has some potential for use as a town theme with some cutting https://www.youtube.com/watch?v=sWW7pfXlYLY (non-PD recording, I'll say it on all of them).
Flee as a Bird has potential too (some people's also non-PD rendition: https://www.youtube.com/watch?v=hCjDnkHuHoY)
I went through a long (extremely long) list of public domain music scores in the last 6 months trying to identify possible music for games. I don't recall all of the sources but I can probably post a list of some of the more popular and commonly heard public domain music (recordings under their own license, not the same as the score of course).
One famous (and oddly hard to identify for non-musicians) collection of scores is the music from Pier Gynt (composer Edvard Grieg). The most notable pieces are suite #1, La Manana (Also known as The Morning in English), and In The Hall of The Mountain King.
@Redshrike
I wasn't familiar with Faure, but I have to say he sounds a lot like Uematsu (or, more correctly, it sounds like he influenced Uematsu).
Links to his musical scores:
@William.Thompsonj
I thought of both of those songs, but I didn't know what they were called, so thank you for finding them. :)
IMSLP links:
Also, just another little bit of inspiration as far as the kind of fun you could have with these songs, here's a disco remix of Also Sprach Zarathustra, from the Little Big Planet 2 soundtrack. Obviously this is copyrighted. :)
https://www.youtube.com/watch?v=NZWX-VBhUFc
I've got something of an addiction to making Midi versions of classical music - working on beethoven's Eroica right now. I have a...lot... of stuff.
These aren't necessarily going to sound any good on your computer, because you are probably using the default midi synth and soundfont - try it with SGM 2.01, sounds really really awesome that way - it's just that the converted files are rather large, possibly because they're .wav
although I did just listen to the entirety of Pictures at an exhibition with the default and still liked it, so...
comments:
Pictures doesn't have every last one - I stopped somewhere at the beginning of baba Yaga. But it's still got most of them and they're kinda awesome, so here it is. - http://www.youtube.com/watch?v=FsvpFU7KY7E there are a lot of different bits, with a lot of different moods.
Death of Ase is from the same suite as morning mood and in the Hall of the mountain king - http://www.youtube.com/watch?v=2aKxf1h5r4g
march slav is a sort of dark march that tchaikovsky wrote - and yes, it builds like 1812.
https://www.youtube.com/watch?v=5poSw7tFLB4
Here, I have an mp3 version of my beethoven's seventh, wnd movement midi - so you can hear how good it sounds. and the midi itself. There's a part that's good for walk, and one that's more serious - it was featured in the King's Speech movie.
I have a lot more.
MountainKing.mid 60.9 Kb [21 download(s)]
PicturesAtanExhibition.mid 617.7 Kb [6 download(s)]
MarchSlav.mid 294.8 Kb [10 download(s)]
beethoven72.mp3 7.7 Mb [10 download(s)]
beethoven'sSeventh.mid 45.8 Kb [9 download(s)]
@Bart: Flee as a Bird isn't Faure, it's a traditional funeral song (likely brought over from Spain).
Musopen has huge library of PD recordings.
Here are links to recordings of few of the mentioned songs.
The Planets:
https://musopen.org/music/search/?q=the+planets
William Tell overture:
http://musopen.org/music/461/gioachino-rossini/william-tell-overture/
1812 Overture:
https://musopen.org/music/190/pyotr-ilyich-tchaikovsky/1812-overture-op-49/
Morning:
Aase's Death:
In the Hall Of The Mountain King:
https://musopen.org/music/1568/edvard-grieg/peer-gynt-suite-no-1-op-46/
There's of course much more and quality of recordings varies.