Tech Wishlist: Data Backups

I wish there was an elegant solution to data backup built into operating systems. I create data, store it in various places on the hard disk, backup some of it occasionally, and then when I get a new computer I burn a bunch of DVDs and try to backup everything. Once my new computer is setup, I don't usually bother to restore everything because I don't want to clutter my new system with things I probably won't need. There are a couple problems with this:

1.Because I don't backup frequently, and because my coverage is spotty, there's significant risk of losing data.
2.Because I don't restore everything, and because the organization of my backups is mediocre, even if I wanted to find some old data, it might be extremely time consuming.

It's not really clear to me how to solve this problem, but to summarize my wish, I want a system for storing that that:

1.Makes backing up automatic so that there is very little risk of losing data and doesn't require remembering to run the backup or the time involved in setting up / performing backups.
2.Readily searchable so that years in the future, finding an old document is relatively painless.
3.Doesn't run the risk of "expiring" the way physical media can do. ie. DVDs only last so long, etc.
4.Is off-site so that a fire (etc) doesn't result in losing everything.
5.Makes setting up a new computer "painless" with respect to "restoring" data.

It's pretty clear that the cloud is an important piece of this puzzle, so perhaps that's why this either doesn't exist or isn't in common use. That, and lots of bandwidth. Perhaps the biggest challenge here is the organizational aspect. ie. It's nice when you get a new computer not to have the clutter of the old one, but if your data repository lives forever in an integrated fashion, then you don't get that nice clean start. So the question is, how can the OS / data repository encourage really good organization of information and purging information that is no longer pertinent, etc? That sounds like a pretty challenging problem to solve.