It depends. How much do you need to back-up? If it's terabytes, I'm guessing rather a lot of that is not unique content that you can't just re-download.
As for reliability, if you stick with Verbatim (I can't recommend any other brand now, because virtually all of them are just relabeled Ritek or CMC), it should last a pretty long time. (Not that Ritek is so terrible: I've yet to encounter an unreadable disc, but I always burned at a conservative speed, and did a verify after writing.) Cost isn't bad: a local chain has packs of 50 Verbatim on sale for $13 several times a year. For really important stuff, I'd burn two copies, using different types of media just to be safe.
Hard drives are great, until they die, and then you don't just lose 4.7 gigs, or perhaps just a couple of files, so I wouldn't rely on just one copy for long-term archiving of family photos and records. But it would be smart to have a portable drive at home which you make a back-up to daily, then swap it once a week for a second USB drive that you keep at the office, so as to be protected from fire and theft. If your backups will fit on a thumbdrive, it might be reasonable to keep the offsite backup stashed in your car or purse.