First things first since so many people make this mistake, RAID is not backup. RAID is redundancy for your live data (with the exception of RAID 0). If you corrupt your OS, you have a redundant corrupt OS. If you get a virus, you have a redundant virus. If you accidentally delete some data, you have a redundant deletion of your data. If you have a fire in the building, you have a redundant hard drive on fire. Yeah, I'm sure you get the picture, and I apologize for belaboring the point. But it's a good point.
For very small users and most home users, tape does not make sense. A single hard drive, CD, or DVD with a copy of the data is usually enough protection. Also home users do not tend to create as much data as business environments that have multiple people working many hours a day. Since a single hard drive is only a bit more expensive than a single tape, nevermind the cost of the tape drive, this usually makes a lot of sense to the home user and some small businesses.
In the case of a small company backup scenario.
You can backup lots more data to a tape drive than to a hard drive, for the simple reason that you can exchange tapes in the same drive. Tape is also a lot safer to transport offsite, which is a must for true backup.
For a simple comparison of capacity, assume LTO3 drives. Those tapes hold approx 400GB uncompressed and compare it to a 400GB hard drive. A tape at newegg costs approx $80, while the comparable hard drive capacity costs $180 for an internal drive.
You have $100 price difference per piece of media. For real backups, companies will keep an entire month's worth of tapes that they cycle through. This means about 30 tapes that are rotating in and out each day. Then you keep your full monthly backups, which amounts to 12 tapes. 42 tapes total. That total for a single year of savings runs about $4-5k for about 40-50 tapes, which is a net savings (even with the cost of a single tape drive which usually runs around 2-3k). Factor in a few years worth of use, and your savings continues to grow. That part is a simple numbers game.
There are a number of other factors that I have not brought into play. Government regulation and compliance can require that you keep a lot more data and for a lot longer than my simple example. Large scale backups in the range of multiple-TB capacity per night usually use a storage hierarchy of disk and tape - disk for speed, tape for cheapness and transportability. I did not factor in multiple copies of the tapes or disks, replication to a backup site for failover, archival of old data, onsite backups for critical machines, or any number of factors of which I have forgotten or am not aware. This also does not include any of the additional hardware that you might need, whether it be a tape robot, disk array, SCSI or FC HBAS, cables, FC or SCSI switches, dedicated network for backups, etc.
Both disk and tape have their place in the day-to-day backup world, it's just a matter of knowing the strengths of each and how to make the best use of both in the particular environment you are in.