Are tape archives still used?
Solution 1:
The Windows Server Backup software that comes with Windows Server 2008 no longer supports backup to tape.
However, there are plenty of third party backup tools for Windows which still support tape. For large volumes of data I don't there's an obvious competitor for tape yet. Something like LTO which can store 800GB a tape combined with an automated tape library can easily provide huge quantities of backup storage.
Tapes are also more convenient than HDDs for off-site storage.
Solution 2:
The Large Hadron Collider (LHC) of CERN is a good illustration of what large amounts of data means: according to that article they expected to collect 15 PiB of data per year that it is operational. And that's only the raw data registered during experiments with the LHC, not interpreted data generated with software by scientists trying to do something useful with it.
They have all this data on a distributed storage system based on hard disks (you can compare it with something like Amazon S3, but they built their own "cloud storage"), but the backups are on tape, simply because that's cheaper.