I'll give another vote for Smugmug. I understand there's always the chance they'll go away, but for now, they tout themselves as a backup solution. All of your photos are replicated across their servers in three different locations.
Never underestimate the need for an offsite backup. You can spend all you want on local backups at your house (I backup between three different machines in my house), but in the event of a major catastophe, they could all be gone. Having our pictures somewhere safe is worth the money I pay to Smugmug. I'm not saying they are the end all be all, but they're what I'm familiar with.
The other suggestions here are good as well, but keep in mind the limitations of each. CDs and DVDs are nowhere near a solid backup platform. Yes they work, but they can be damaged or have other issues over time. They also become a hassle when your collection exceeds the disk size. I like the idea of using a couple of USB drives, with at least one being kept at work (again, for an offsite backup). Of course all of these are only as good as you are about actually doing the copies and backups.