I Tunes Backup

Backing up to double-layer DVD's is certainly better than having no backup but it's a fair amount of work to burn the discs, keep them organized and to restore them if you have to do that. If you're going to do it that way I'd suggest you make two complete sets and keep one offsite.

As Kennyt says, hard drives are really cheap now, I've seen 1TB drives for even less, around $125, and you don't need to go to the trouble of setting up a RAID array to have an effective backup.

I have an external drive of the same capacity as the one that holds my music and use the application 'SuperDuper' to clone my regular hard drive by plugging in the external one every weekend and doing an incremental backup. After the initial copying of the drive it takes only 10 or 15 minutes, depending on how much music I've added over the week. There's always the risk of losing one week's worth of music but redoing that amount of work isn't very scary. I'm paranoid enough that if I leave town for a few days I put the external drive into a fire-proof safe in my basement.

I bought a Drobo and Drobo Share which is basically infinite storage with self-contained back up. I have pathed my iTunes there, and it currently has 4TB drives in it. That gives me 3.2 TB of storage, and backs it all up. If any of the drives fails, Drobo tells you to replace it, and you just plug in a new one. I don't back anything up past this, because it backs it all up internally. Really a great invention.

I use a Cavalry 1TB external HD ( mirror back-up system). It wasn't cheap, about $450, but all of my iTunes library is backed-up on it and sitting on the shelf. Since the entire library is also in iTunes on the iMac internal HD there is no need to keep the Cavalry hooked-up. Once the library exceeds the iMac internal HD it will be necessary to make choices as to what stays in the iMac and what is listened to only when pulling it from the Cavalry. My library is about 525 CDs strong and growing. Since getting the Cavalry I no longer burn back-up copies of CDs.

I use a Western Digital - My Book Studio Edition II 2TB External USB 2.0/FireWire/eSATA Hard Drive with my Mac Mini. It has two, 1 TB drives and it's is mirrored like Puerto's. It's Mac compatible and has easy to follow set up instructions.

http://www.wdc.com/en/products/Products.asp?DriveID=410

Don't count on DVDs, especially dual layer dvds. In my experience, (i owned a prepress service business, archiving gigs of data every day for clients) average off the shelf DVDs had a pretty high failure rate, around 18% when stored in jewel cases in a climate controlled environment for 1 year. Dual layer were worse. I did find however that archival DVDs (single layer Mitsui gold to be specific) stored as above have had a 100% data retention rate thus far. At more than a dollar a pop when bought in bulk they're not cheap, but a decent option. Still as stated by others, an external hard drive is your simplest if not least expensive option.