I usually play generic ambiental music or soundtracks in the background. However, in my last campaign, I had one session which was entirely devoted to music - the party bard had to go through a "musical maze" to locate a source of the True Song (q.v. Seeker of the Song prestige class); each twist in the maze was represented by a different sound-based creature (harpies, sirines, abeils, etc.) and he had to find a way to suppress the creatures' sound effects to be able to better hear the background music of the maze and locate its source. I hand-picked each creature's theme song and played it during the encounter (IIRC, he resolved all but two of the encounters, and he only resolved one through combat).
To make the session fun for everyone, I handed over control of the creatures to the other players, who had fun trying to deter the bard from his quest.
Here are the themes I used:
DESTRACHAN
Michael Hoenig - Baldur's Gate, The Last Battle
HARPY
E.S. Posthumus - Ebla
SATYR
Greensleeves
SIRINE
Heroes of Might & Magic 2, Ocean Theme
MUD SLAAD
Mark Morgan - Planescape: Torment, Ravel’s Maze
LILLEND
Debussy - Clair de Lune
CRYPT CHANTER
Saint-Saens - Danse Macabre
GALEB DUHR
Jeremy Soule - Icewind Dale, Kuldahar Valley Theme
FIRRE
Heroes of Might & Magic 2, Sorceress Theme
ABEIL QUEEN
Rimsky-Korsakov - Flight of the Bumblebee
TRUMPET ARCHON
Wagner - Ride of the Valkyries
WIND GHOST
Ennio Morricone - Le Vent, Le Cri
SONG DRAGON
Beethoven - Ode to Joy
DEATH KNIGHT
Heroes of Might & Magic 2, Necropolis Theme