I'd suggest listening to the words carefully and determining if they speak things you agree with. I listen to a fair amount of secular music myself, and some of them are simply powerful songs about emotions, which I find OK. There's nothing wrong with singing about struggles and not knowing where life is taking you, because those are concerns. Off the top of my head, songs like "Crawling" and "Lying Away From You" by Linkin Park are very powerful songs about frustrations with one's self and dealing with tough situations. Neither really gives a negative message, but I feel they leave you with the hope that better times lie ahead. I find it important to communicate these feelings, because we do all deal with struggles in our lives, believers or non-believers.
But then again, there are songs which hide dark and destructive messages in with great music. There have been a lot of songs over the last few years I have gone back and listened to the lyrics again only to find that they don't allign with my views on God and life any more. The beats and musicianship were so lucritive that I just glazed over what was being said. I find this the case with a lot of radio music, and I often catch myself later.
I guess what I'm trying to say is to listen with discression. Don't just throw out all secular music, because God may be trying to speak to you through it. It wouldn't be the first time He attempted to contact one through a non-believer. But don't accept all of it either, because Satan will produce seductive sounds to try and keep people from seeing God.