Go have a look.

http://search.yahoo.com/search?p=on-line+archival+service&ei=UTF-8&fr=moz35

Thanks to both for responding.  Barry, I'd seen most of these before and unfortunately they don't meet my requirements.  Velocicarpo, Amazon Glacier looks interesting.  Something I need to look into closer.

Again, thanks to both.

Amazon S3, and the newer, cheaper Glacier version of S3,  can do what you want.  Synchronization is up to the client program.   I use JungleDisk and by default, it just uploads new and changed files, it doesn't delete anything on the S3 side unless and until I initiate a "backup cleanup".

Is there some reason why you must pay for an online service instead of doing it yourself? (for less)

$45 and you can drop in drives or remove them, add new ones, take them to a vault, or have duplicates made by dropping in two drives and hitting "COPY".

1T $89 and probably less if I took the time to shop.

Automatic, offsite backup is a good idea.   If you use an external drive you'll need program to run a backup on a schedule, and it would be a very good idea to rotate that drive with another that's kept at a friend's house.   Never rule out the possibility that someone breaks in while you're on vacation and takes the entire computer.  Or, you could have a fire.

Two Copies, one on site one someplace else. Hard drives are cheap. Since I have everything in two places maybe three at the office, and I'm not all worried about archival storage, it works for me. (didn't I write two copies in the original post? Ah, OK I did...)

What w7lwi is getting at is this. Most backup services are just that. They don't archive, they back up. If you delete all your files on the computer, then they are deleted from the service. Same problem that some people have had when they lost everything on a RAID backup and didn't understand, if you delete everything, it's gone EVERYWHERE.   

What he wants is an archiving service, which would be a great solution.

Best I can do is offer an alternative that works, locally and doesn't keep charging someone month after month.

Next would be DropBox? But same thing, you can connect multiple computers and access it from anywhere. Really nice. If you delete a file, it's gone from everywhere!