I do all my editing on my laptop (with an extra screen attached). The products of the editing are synchronized to my netbook - even though I won't be doing any editing there, it's a "live" copy of the files, and a layer of redundancy.
The next redundancy is an external hard drive. I push backups to the drive on a regular schedule.
My third backup layer is Amazon S3, via JungleDisk. Set it and forget it! Costs a few dollars a month for the used space, as well as any additions.
I used to do backups on CD/DVD, but that was a clunky process, and the common wisdom is that such media can degrade over time, and may not be the most trustworthy. Hard drives are better in longevity, as well as capacity.
Floppy discs - hah! I doubt I could fit more than a couple of photos on one of those! Seriously, don't even bother. They are small and error prone, and most computers these days don't have floppy drives.
Flash drives are compact and inexpensive, true, and may be suitable if you do not have a particularly large volume of files to back up. But, again, for large capacities, hard drives are the way to go.