If it's DRM-free music, it's the same way as for all other files, like:
- burn to CD or DVD
- copy to USB-stick or external hard disk
- direct cable connection or home network
- copy to and from a shared storage site on Internet
- mail to yourself as an attachment
- copy to and from your mp3-player (a 40 Gb iTunes does fine, probably)
It might be a little bit more complex if:
- it's DRM'ed music that won't play on another PC by default (because it's tied to your current computer)
- you want to transfer not only the music files but also the music library with all meta data (like playlists)
In that case, it depends on both the media player you use and the site where you bought those music files. And without knowing those small details, nothing specific can be said.
I am currently using a Dell Dimension 4600 with Windows XP. I am planning on purchasing a new computer at some point in the near future. My question: How do I go about transfering my downloaded music from the old computer to the new one?