How much do you expect to initially store, and what rate will this increase? What upload speed do you have on your connection?
Ideally, if you have a good upload and are only storing stuff like images, using a cloud based storage like Dropbox is the best solution - It's automated, and easy for you to get to your pics anywhere which might be nice for sharing them with other people. It's also pretty bulletproof - they use multiple backups and replicate across continents.
If cloud storage isn't suitable, then rpstewarts suggestion is safest, but obviously requires a lot more effort to keep on top of, and if your house burns down you'll lose whatever you hadn't backed up to the offsite location.
After that keeping the data on two different devices in your house is next safest, A NAS caddy and synchronized folders is better than a RAID array. Cost you less than £20 for a simple one and has the added benefit of being portable - you can take it round to a relatives house and use it like a USB drive.
RAID is pretty vulnerable, RAID5 itself can suffer from corruption, so you're better off with a mirroring level, like RAID1 or RAID10. Still the data is vulnerable to power surges/PSU failure taking out all the drives, and if a file is deleted by a virus/human error, there's no backup. It's also vulnerable to fire/flood/theft etc.
Personally I run an 8 drive RAID5, couple of drive failures over the 6 years i've had it, but rebuilds were fine and no data lost. I've recently built a second file server to replicate the more important stuff. Documents etc I keep either in google docs or my free dropbox account. The setup should do me the next 5-10 years until FTTH arrives with gigabit uploads and I can move to cloud storage.