Ideally, you always want a system (speakers, amps, room, etc) that can accurately reproduce the complete frequency spectrum of human hearing (around 20Hz to 20kHz), but this is not always possible, so building a system that favors your musical taste is a good idea. Knowing where to make sacrifices and where to re-enforce can make a big difference.
For example, if you are mostly into simple guitar-voice Nueva Trova (a genre that features guitar and voice prominently, often exclusively), you might want to pass on a subwoofer and focus in the other ranges. Lowest guitar note is normally around 80Hz, the human voice is normally above 100Hz, and subwoofers normally reproduce frequencies bellow 80Hz, so a subwoofer here isn't doing a lot of work, it wouldn't make a huge difference.
In contrast, if you are mostly into electronic music genres, which normally have a lot going on bellow 80Hz, a subwoofer will make a huge difference (as in night and day difference).
Every part of an audio system (not only the speakers, but the amps, the room, your complete listening environment) has a characteristic sound. Some have more bass than others, some have more treble than others, some distort less than others, etc. Try to aim for a system that suits your musical preferences.
We are talking about frequencies here just to make a point, but the best way to decide which speakers to buy is to listen to them. Grab your favorite songs and test them through different speakers (any decent store will let you do this). They will not sound exactly the same in your living room, but it will get you a good idea of their character.