When I shoot, I record my images to two cards at once, so I start with a backup in the camera.
When I'm home, I use lightroom to convert the RAW files to DNG and copy them to two different hard drives in my computer (actually, one hard drive for backup and a 2-drive striped RAID for editing). Once that is done, I put the cards back in the camera and reformat.
When I'm done culling (which usually means deleting between 50% and 90% of my shots) and editing, I copy the final DNG files and PSD files to a RAID5 (sort of) NAS. I also put JPG's in another folder on another RAID5 NAS. I sometimes upload the JPG's to Smugmug as well.
Once a month (or so), I archive the DNG and JPG files to two sets of DVDs using ArchiveCreator. I keep one set of DVDs at home and one at the office. At that time, I usually wipe out the local copies of the files and repoint Lightroom to the NAS versions.
At no time from when the camera flushes it's buffer onward are the files stored on any one disk. Drives fail. For the long term, I keep three copies - the DNG and JPG files on the NAS boxes, the DVDs I keep at home, and the DVDs I keep at the office. Honestly, I'd be pretty comfortable with the two DVD copies, but I like having the files available online as well.
I would not consider dual hard drives a reasonable long term storage solution. I would definitely not consider a single hard drive to be a reasonable long term storage solution.
When traveling, I usually back up to a laptop and burn a copy from the laptop onto a DVD before wiping the memory cards. If the outing isn't all that important, I don't bring a laptop and just leave everything on memory cards. I'm about to order a 16 gig SD card and a 16 gig CF card so that I can handle any single day of shooting without fussing with cards.
My rules are - redundant copies of the pix are a must. It's too easy to accidentally delete a picture even on a RAID. DVDs are more reliable and last longer than hard disks if you don't use them much. If you frequently mess with your DVDs, they get scratched and aren't as reliable.
RAID arrays are nice, but they aren't really all that great from a backup perspective. I've seen two drives in a RAID fail before.