Dropbox should work here, but it's simply too expensive. My photo library is 175GB. That isn't excessive when considering I store the digital negatives and this represents over a decade.
I don't mind not being able to access it for a few hours, I'm thinking disaster recovery of highly sentimental digital memories here.
If my flat burns down destroying my local copy, and my personal off-site backup (HDD at an old friends' house) is also destroyed... then nothing would be lost if Amazon have a copy.
In fact I very much doubt anyone I know that isn't a tech actually keeps all of their data backed-up even in that manner.
I find myself already wondering: My 12TB NAS, how much is used (4TB)... could I backup all of it remotely? It's crazy that this approaches being feasible. It's under 30GBP per month for Ireland storage for my all of the data on my NAS.
To be able to say, "All of my photos are safe for years and it's easy to append to the backup.". That would be something.
A service offering a simple consumer interface for this could really do well.