if we are talking bout general background soundtrack the, almost all games should have it, if you mean like actual song in the background , it depends on the setting and type of game,but i rarely find a game with music that detract or get in the way.
I won't play a game if I can't turn off music and ambient sounds. Active sounds like footsteps and interaction are fine, though. A bard in a tavern playing a tune is fine, but manditory metamusic is a game killer for me.
Ye sure, games should have music but also the option to turn it off, it makes them more fun and exciting for me, music helps create a better atmosphere