The biggest problem with harddrives is moving them, and you don't know if they'll ever spin up again once you unplug them. And for those people that consider a single USB harddrive a backup device, you're not thinking in terms of large volumes of data or any form of scalability. (Try shipping your disk array to a bank safety deposit box).
The biggest problem with tapes is that they are slow and they get damaged during moves, just like harddrives. Also, the drives, robots, infrastructure, and maintenance to run your backups are very expensive.
In order to overcome the slowness factor of tape, many companies run nearline disk arrays as part of their backup process. They backup to disk overnight because disk is faster and will shorten their backup windows. During the day, they move their backups from disk to tape, with at least 2 complete sets of tapes. Some of those tapes are shipped offsite. Others are kept onsite for restores.
Another alternative is offsite replication. This is the one case where disk completely trumps tape. However, you have to determine if your bandwidth costs and hardware duplication costs are going to be less than the cost of maintaining a tape system. I've seen this justified by the additional benefit of turn-key site failover. It's a rather slick solution, but if you thought tape was spendy...
Disks must overcome their mechanical design and would have to drop in price greatly to competely replace tape. For now, tape still has its place.