Bryan, everyone used to store their stuff on floppy disks or tape but a lot of that is now unreadable, either due to new computers being unable to read the format or because the actual media has deteriorated. Not all CDs are the same, some are better quality than others. CDs will be around for a while yet but look at the advances we are already seeing, DVDs, dual layer DVDs, Blu-Ray DVDs - all with bigger capacities. At the moment there is a fair degree of backward compatibility with the hardware but at some point conventional CDs will go the same way as floppy disks. So, every so often you will need to change your backup media. In my case, all my important stuff is on my PC and the CDs/DVD are effectively just transient backups. My main backups are to external hard disks.
As long as you keep the primary copy of all the important stuff on your main machine you will always be able to back it up to whatever the current flavour of secondary storage is. The danger comes if you move important stuff you want to archive onto a CD/DVD to free up room on your PC. Then the "backup" you have made becomes the primary and maybe only copy and if you leave it long enough then you may find you can't get it back if you need it.
As far as music is concerned, CDs are rapidly going the same way as vinyl now as everyone buys Ipods instead which can hold all the music you want and link to music libraries on your PC. It won't be long before new cars don't come with a CD player any longer, there will just be an IPod connector.
So, to respond to your question; there isn't a really long term answer (unless you build a pyramid or something), you just have to keep running to stay up. Yes, it is potentially scary and it's an acknowledged problem.
A longer (as opposed to long) term solution is seen as being Cloud Computing where your data is stored and backed up over the internet.
Colin