If you're monetizing the video, look to the creator of the original song. In the case of something that's actually on the radio...ehhhh, don't get your hopes up, you'll need to contact the band or the producer of the song, someone who OWNS it. If it's something lesser known or even a local band, you'll have a lot more luck, as I've found that many of them are excited to have you link to them and give them viewers through you.
From a personal note, we've tried putting in remixes of "Vampire Killer," the 8-Bit theme of the game "Castlevania," as well as the original song, and both times we we're declined for monetizing. We are working on getting a friend to do a personal remix of the theme, but even then, since it's based off of the original song, I don't know if we will be allowed to monetize a video with that as well. All of our other videos seem perfectly fine.