I ran into some articles that suggested that burnt CDs degrade after 2 to 5 years. I have heard of people saying that CDs that they purchased began to degrade after about 20 years. It was recommended that I find some magnetic tapes for long-term storage of my files.

The products I have run into seem to be geared towards businessess that need to store their data on 3 terabyte tapes. As I anticipate only needing to store about 200 gigabytes of data, I am wondering what products exist for people at home. I just need a starting point for my research on this subject.

Use software RAID1 disk storage. Reasons:

- Software RAID is independent of a specific manufacturer continuing to manufacture a compatible product.

- Disk drives are faster than tape, both for backup and restoration.

- RAID1 protects you against a drive failure, and can even be supported with a hot spare (a drive that automatically gets switched in when one of the primary drives fail).

- Disk drives are inexpensive in the long run. Tapes should be replaced after they are used 30 to 50 times. People rarely do this, then find their successfully backed-up data doesn't exist when they need it. High capacity tapes can be expensive, when regularly replaced.

- External (hotplug) USB 2.0 or Firewire 400/800 drives can be software RAIDed, making inexpensive hotswap RAID easily implemented for even home users.

I'll add to that, a word of caution:

RAID1, although looking like a great solution, does -not always- work in cheap home user external USB/Firewire harddisk enclosures that are advertised to have that function. They often employ STRIPING techniques, which means data is spanning multiple disks: If one drive fails, everything on the RAID1 set is lost, and you'll be one sad angry monkey. And I do mean sad and angry here, and I think you'd know why.
The best RAID implementations are made with a computer and at least one hardware based RAID card plus two good quality drives (As opposed to RAID cards that are backed by software, which put the load on your computer's CPU and RAM instead of relying on their own CPU and RAM like true hardware based cards), or a dedicated external (headless) storage unit based on such hardware. The cheapest RAID cards are usually software based (You know, those $20 cards). Cards in the range of $200~$500 are more likely to be hardware based (have their own RAM, also known as Buffer memory, and their own CPU on the same card), ask around because there's a lot of brands out there that make these cards (try Adaptec's site for example).
In the long run, hardware based cards perform best. At work I have two Adaptec SCSI RAID card with 32MB buffer + CPU which have been running for over 5 years straight now on a 24/7 basis.

For more information about RAID, see this article on Wikipedia and this interactive diagram.

I agree most of what macemoneta mention except RAID-1 increases the complexity of backups. Backups are a complex process even though books say it is a piece of cake. I do full backups instead of incremental and differential backups because full backups are the easiest but they take longer. I recommend using mobile rack enclosures instead of USB and IEEE-1394 to ease the backups. If backups are easy, you are going to do it more often.

DVD disc should be used for backups instead of CD if you are going the optical storage route. DVD dics contain two areas where data is kept. One is the data and the other is ECC. CD do not have ECC, so a scratch or a bad write can easily make a coaster. When data on a DVD disc is partially corrupted, the ECC data can be used to reconstruct the data. Do not place a label on the disks because it damages the dye over time and the label can come off in the optical drive. Use an ink jet printer to create the label which creates a quality label that can never come off. Depending on the quality of the disc. They can last up to 20 years or more. Use archival type disks, but the quality of the archival discs depends on the firmware of the DVD recordable drive.

Does a RAID have to be continually running, or is this something that I could leave in storage or in a safety deposit box for 20 years? It seems to me that there should be a readily available product for this, as many people have switched to digital cameras.

No storage medium is going to be acceptable, untouched, over a 20-year period. The problem is that technology changes, and finding compatible equipment over even that relatively short time span is difficult. Important data must be periodically migrated to new storage.

RAID is a technology that ties harddisks together. If for example you have a mobile rack that employs RAID technology like Electro suggests to ease your backups, sure you could disconnect it and put it in safe storage for as long as you'd like. But remember that lugging around a machine by the weight of a family bag of large potatoes may not be that conveniant.
Some racks however give you the ability to remove individual drives (Hot swapping) and replace them with spares, much like you would change a server's a backup tape every morning for a fresh one, and putting the one you took out into the tape safe.
With a rack like that you'd be good for the next 5 to 10 years perhaps but not 20 years, technology changes too fast for that and you'll have to keep in mind that while these things are far more sturdy than a CD or a DVD backup system, they are still at risk of faillure and may need upgrading/replacement/repair some day.
[Edit: macemoneta said that last bit already. ]

Have a look here for examples of rack enclosures that have RAID technology:
Promise Technology drive enclosures
You'll notice that these are meant for being mounted into a 19" server rack, so if you're looking for a home desktop equivalent you'd be more interested in the following:
Promise UltraTrak SX4000 4 Channel External RAID Enclosure

General: I had to chuckle when I read your comment about safe deposit box storage, because I had the same problem.

My main rotating backups are done to large USB drives which are stored off-site, but there are things that for business reasons need to be stored in a safe deposit box. The tradeoff between cost, capacity and physical size I chose for that purpose was to backup with/to AIT-1 drives/tape. The larger tapes are 35GB uncompressed with compression typically maxing out around 90GB, but expect less.

The AIT-1 tapes can be read by almost any AIT-style tape drive, so you should be able to access them for some time into the future. But even tape will (eventually) degrade in an environmentally controlled safe deposit box, so there is a finite storage limit.

Although the AIT-1 drives and tapes are pricy retail, you can find some outstanding deals for them on ebay if you look hard. You can also find lots of “Are they out of their minds?” deals there, too, so look carefully.

The newer AIT-1 Turbo drives are another option, as they can use very inexpensive tapes without the memory chip present in the AIT-1 tapes. But you will likely pay retail price for those drives and tapes.