There's no one answer to this. Some genres you love because you associate them with a person, place or time, others resonate with you for unknown reasons, and others you hate until one day you suddenly love them.
In general, I'm always looking for new music, and here are some of the places I typically find it: Checking out a new radio station, looking up "best of" lists on the internet, talking to friends about music and following up on their suggestions (or trading mixes with them), going to see live bands, surfing for music videos, reading about music in magazines and online, following the links in questions here in this forum, and (my most productive method of recent times), downloading free samplers from Amazon's digital music section. Keep in mind that you often have to give the best music a while to settle in before you know how you really feel about it.
Of course, a lot of people find music these days through personalized stations, like Pandora, but I usually find I never hear anything fresh and unexpected that way, at least not on my own stations (The one exception, oddly enough, is YouTube's personalized suggestions. For some reason, YouTube seems to have really nailed my musical tastes in a way that has eluded the other services...)