If you copy the entire music folder (not just the one with the songs, but the one with the xml and itdb databases as well) such that everything stays in the same standard position, it should find it on the new machine (I do this all the time). If you’ve separated your Music folder to somewhere non-standard (usually a different drive so you don’t have to keep it on your user drive), you can re-point iTunes to the actual music in Preferences->Advanced->iTunes->iTunes Media Folder->Change…
That does assume you let iTunes make a copy of your music when you added it to the library (the default). If not, you will have to re-add each time: a good argument for letting iTunes make the copy (hard drives are dirt cheap, and you don’t need the original after the copy, so you can have all your media sources point at the iTunes Library – you don’t need to keep duplicates of everything).