Some sites are fine. You can buy music online, from a secure site without worrying about your computer. You can also download demos from places such as MySpace or a band's home page. While there can be viruses attached to any file, these sorts of downloads are relatively safe.

Another safe way to download music is to email files back and forth with friends (following the rules above) but these take a long time to attach and open. 
File sharing music is a completely different thing. File sharing is extremely risky and legally and morally questionable.

Rule number one for protecting protect yourself from downloading a virus when you download music is to not use any file sharing software. File sharing software is spyware. This means that by using file sharing software, you are giving people, possibly bad people, access to your computer.

If you want to break rule number one, buy the best anti-virus software that you can find. Make sure it includes anti-spyware, anti-adware, anti-malware, and a pop-up blocker. However, file sharing is playing with fire. If you don't want to get burned find another way to get your music.