You can copy all your songs on an external harddrive and copy it on a new computer. Just copy the whole music folder on your external harddrive. Than connect it to your new computer and move the folder if you wish on the harddrive of your new computer (on a Windows machine move it to "My Music" folder on Mac OS X to "Music" folder). After that launch Itunes and import the whole folder you just copied. Done. If you play a song you bought in the Itunes store Itunes will ask you if you want to authorize your new PC to play bought songs. Just enter your Itunes login and password and that's it.

You can play your bought songs on up to five PCs. You can reset the counter for the five PCs once per year. It will de-authorize all your authorized PCs. The next time you play bought music on Itunes it will ask if you want to authorize your PC and the counter starts again.