A mass restoration is expected to be rare, so it's okay for it to be a bit more expensive.
edit: 45tb for 300€/month: https://www.hetzner.de/en/hosting/produkte_rootserver/xs29
If so, that's still less than €8/TB/mo, which is better than most cloud storage providers offers. You also have some spare memory and CPU resources (so you could resell them for others as, for example, memcached instances) and a possibility to get a proper SLA, as a bonus.
1. Regularly back up "important" directories (code/, papers/, web/, etc.) to fairly safe/redundant cloud storage with incremental history. I have pretty little of this, <50gb, so it's not super-expensive.
2. Occasionally exchange bulk but less-important backups with my brother, so we're each the other's high-latency, questionable-durability "off-site backup". No incremental dumps here, just rsync. This is where my MP3 collection, DVD rips, and similar goes.
3. Photos, which are important but also bulk, go to Flickr, which is free.
4. Don't back up stuff I can re-acquire, e.g. big public datasets I've downloaded to work on, or Debian ISOs. Also, I don't back up the OS, just my data.
There do, however, seem to be some cloud services that offer big full-disk backups for a surprisingly low flat price, e.g. http://www.backblaze.com/ is $5/mo/machine.
For backups, you're dealing with a relatively consistent or predictable amount of data. Buy the appropriate dedicated server for your needs.
What I'd consider is essentially the Crashplan model: P2P / external backups locally (i.e. full LAN speed) and an off-site replica which can be cheaper and slower as long as you have a high confidence that it'll be available eventually. This way normal operations are fast but if the building burns down you're covered and presumably have higher priorities than waiting for a restore to run.
Anything is possible with money, of course, but how is this anything other than really expensive?
For example AWS S3 would be $235/month (that's $2,820/year!) for 3TB not even including any data-out transfer charges. Sure there are others that are cheaper but only marginally so.
Is this really what people are doing? Makes the commercial services sound really cheap.