If you really don't want to rip all of your CDs again, I'm going to recommend a multi-prong approach:
1) Keep them on your internal hard drive. Not only will they be convenient for listening, but they'll move to your next computer along with the rest of your data.
2) Make your Music folder part of your regular, daily backup routine. That way, every new song will be backed up soon after you acquire it.
3) Get an MP3 player with a large enough capacity to fit your entire music collection, and transfer everything to that. More listening pleasure, and an extra copy.
4) Burn it all to DVDs, as data, not as audio. In other words, copy all of the files, as files. Use expensive, gold-backed Archival DVDs. Store them properly, upright, in a cool, dry location.
5) Burn another set to DVD, and store these somewhere else. Or ask a friend to store them.
That gives you five copies. One of them will survive.
Read the original forum discussion.