There are two things necessary for the subwoofer to be good for music. One is mentioned by Warpdrv; you need a good quality one for it to sound good. The other part that most people bungle is properly setting it up. Many people like to turn it up too high for a flat frequency response, because they like the rumble of explosions to be louder than the sound engineer wanted them to be. This gives them an unnatural, "boomy" amount of bass with music, which is less than ideal (I think excessive bass is always less than ideal, but obviously there are plenty of people who want more bass than what is mixed into the sound). If you have listened to the typical home theater system, this is what you have likely encountered, and it has likely caused you to believe that subwoofers are bad for music.
If you want accurate, deep bass, set it so that you have a flat frequency response. I have two SVS CS-Ultras (these are the old 12" woofer Ultra cylinders, and they are unpowered, so I use a separate power amplifier to drive them). I set them to give me basically a flat frequency response down to about 15 Hz. There is nothing like truly deep, flat bass response. I have never heard better bass on anyone else's system.
If you listen to music that actually has deep bass (e.g., some pipe organ music, etc.), then it will make a very significant difference, and no "full range" speaker that does not go flat down below 20 Hz will ever sound as good as having a good, properly set up subwoofer.
The thing is, a separate subwoofer gives the user the option of screwing up the sound by not having the balance between the subwoofer and the main speakers correct. (Just imagine how it would be if everyone had a separate powered woofer, powered midrange, and powered tweeter, and set the relative volume according to personal preference; very few people would set it properly for a flat frequency response.)
