I remember the days of Napster when we all lived in ignorant bliss. Any music you wanted for free. Those were the days. But honestly with the websites around nowadays you can still listen to just about any song you want for free (legally too). You just can't download it. Most people already know about Pandora. Pandora has created the music genome project where you can create stations based on any artist or song, then it will continue to play music similar to that. You can customize each station by adding new artists or saying whether you like a song or not. That's usually what I listen to at work. I like the variety. And it has introduced me to some great new music I wouldn't have listened to otherwise. I am now up to 22 stations on Pandora. Oh, and to get rid of the annoying advertisements just use Firefox and download the ad-block plus add-on.
Two other sites let you look up any song you want to listen to. The first is Project Playlist. I used this one for awhile. Lately though, I have been going to Seeqpod.com. This site searches all audio files, and video files if you want. It has a sleeker feel than Project Playlist, you can fast forward/rewind songs, search without interrupting the current song playing, and easily create a list of songs to listen to. Check them out and have fun!