GOG.com: NOTE:
This rerelease of Mafia has an edited soundtrack and does not include any licensed music.
NOTED - And thanks for being honest with us ... even with the first description, which some struggled to understand ... most of us knew exactly what you meant ... or should have.
Also thanks for setting up the example structure for reinstating the music or some suitable music.
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Despite what some think about artistic aspects and bastardizing the game by editing the music out, and what some think about illegally re-instating the missing music, all those aspects need never apply.
The missing music was never made for the game, it was just chosen like we all choose our music, and the original atmosphere, despite what some think, is not reliant on those exact original tracks, but can also apply to other tracks from that same period in time. Of course, those who know the game of old, have memories tied to specific tracks, but I am guessing many of them probably have the original discs, and there are no legality issues involved with utilizing what they own. I would say the same for the Xbox etc versions, and so if you still have those discs, then just get a copy from elsewhere of the original tracks, as you have already paid for them. If you have lost or sold or worn out your original discs, well more fool you ... take more care in future, if you really care.
As for those of us who don't own the original discs and have never played the game before, guess what?
Yep, you could go to the sales bin at your local music store and grab some golden oldy CD's from the same time period, and using the names GOG or the Game Publisher (2YK) have provided with their dummy files, replace them with OGG converts of your own. You only need suitable music to get the right atmosphere, not specific tracks. There may even be cheap tracks available online. This presumes you don't already have something suitable in your music collection already, but even better if you do. No legality issues for music you legally own.
Nostalgia is good, but History is flexible, just like everything else ... and no two people see it in exactly the same way.
Sometimes I really despair with the way some people misjudge GOG, and this Game is the perfect example of how they went out of their way to please their customers ... unfortunately some can never be pleased.