Here's as much music from the Final Fight series and related games as I can get. Everything is in MP3 format.

= MIKE HAGGAR AWESOME. I really like this track.

[Capcom Vs. SNK] [Final Fight] [Final Fight Amiga] [Final Fight CD] [Final Fight Double Impact] [Final Fight One] [Final Fight SNES] [Final Fight 2] [Final Fight 3] [Final Fight Revenge]

[Final Fight Streetwise] [Marvel Vs. Capcom 3] [Marvel Vs. Capcom Infinite] [Mighty Final Fight] [Namco X Capcom] [Ring of Destruction] [Street Fighter III 2nd Impact] [Street Fighter III 3rd Strike]

[Street Fighter Alpha] [Street Fighter Alpha 2] [Street Fighter Alpha 3] [Street Fighter X Tekken] [Street Fighter V] [Super Street Fighter IV] [Ultra Street Fighter IV]

As far as I know this single remix is the only Final Fight related music track in the game.

Something Putrid by the Bay Remix

Ring of Destruction has a really good soundtrack. Haggar's theme isn't the best one in the game by a long shot, but his victory theme is decent.

Used in:
New York
Haggar's Stage
Haggar Victory
Winner/Loser screen

Decent music for Hugo which certainly fits his stage.

Used in:
Bottoms Up
Hugo's Stage (Munich)

The way the music works in this game is that it changes between rounds. The arranged version can also be heard in the PS2 and Xbox versions of the game.

Used in:
Hugo's Stage (Home Sweet Home, Arcade version)
Hugo's Stage (Home Sweet Home, Dreamcast version)