I'll add my two cents.
Definitely an external hard drive should be your primary backup. I have a 250GB drive that I use to backup my computer. Since it is external, I also use it to backup my wife's laptop by simply plugging it into the laptop's USB port instead of my desktop's.
I don't mind flash drives, by my data takes up a lot of GB (12+). Most of my data are digital photos that I can't replace if my hard drive crashed. I only use my flash drive for quick backups, as James mentioned, until I can get the hard drive up and running.
My seconday backup are DVD+Rs. There is a difference between +R and -R, and for archiving +Rs are better (-Rs for everyday use). I always burn two copies of my data and keep them both offsite. I only use premium DVD+R discs (Taiyo Yuden) that are reliable and well made so the data should be safe.
My dad's hard drive crashed and he lost a lot of digital photos. I installed a new hard drive and had him go out and buy an external one for backups.
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