when you connect it, you can choose to not sync, and then manually manage the music. that won't erase the songs already on it.

and then, you can always copy the .mp3 files from the ipod to the new computer. if you bought them, you can just transfer them (through itunes). otherwise you can just copy the files that are in the hidden directory and re-add them to itunes (you don't need to worry about the file names because itunes will fix them if they were tagged properly). or there's xplay, or winamp, or others.