Not to be pedantic, but RAID isn't a backup solution - it's a reliability solution. That said, it's the backup solution
I'd run, if I ran one
One day, when I get a real job and actually have money for another decent computer, I'll set up a fileserver with RAIDed harddrives and have my other computers back up data to it -- and I suppose every now and then I'll have to burn DVDs off the backup server. Still, it's a real pain in the ass to do proper backups for a home solution.
For an office solution, you can buy expensive hardware and software and it's not as big of a deal - but there's no good solution for home users. It's just something you have to force yourself to do, even though it's an inconvenience.