Ulfwald, comparing tapes to, say, using a bunch of IDE drives on a network server somewhere else:
Cost:
Pro: if you need a lot of restore points, tape is cheaper (drive is expensive, tapes themselves are cheap, if you want to hold onto two weeks' worth of tapes before rotating them around again, tapes are cheaper than that many HDs, if you don't need as many restore points, then disk is cheaper).
Con: if you don't, you can get a few IDE drives and IDE removable carriers cheaper than a tape drive and a bunch of tapes.
Compatibility:
Con: Tape drives generally require SCSI (unless they reeeeeally suck) and that's not available on just any PC, tape drives are not available on just any PC, and there are too darn many tape formats. So if you lose your backup system and have a bunch of tapes, you might still need a lot of time to get that data back, unless you buy a clone of your backup system or at least tape drive and have it in a safe location.
Pro: Random enterprise/non-low-end backup software is built to deal with tapes, and might or might not deal with hard drive solutions, but probably won't do those as well as tapes
Physical security:
Pro: it's easier to take tapes out and off-site and off-site storage places know what to do with tapes
Speed:
Con: tapes are slow. Manufacturers' performance numbers are typically >2x reality. Soooo slow. IDE disks are fairly fast, especially for linear operations like backups.
Capacity:
Con: very high capacity tapes are expensive, cheaper tapes don't hold much. Tapes hold on the order of tens of Gb these days, but hard drives hold on the order of hundreds of Gb these days.
Longevity:
Pro: My experience is mostly with 8mm and 4mm tapes, and those hold data like forever and hardly ever go bad. The same cannot be said for IDE hard drives!
There are many trade-offs, if you have any other questions, please ask specific questions. I'm a long time tape fanatic. Since 1995, every single year of my life, the hard drive in my desktop PC has died and needed replacement at least once. That's one seriously bad track record, and were it not for backup tapes, this would have gone from very bad to even worse than that.
HOWEVER, these days, I have to say that I'm using disk cloning for backups more than my tape drive. Why? Performance, and capacity. I have a 12GB DDS-3 tape drive, and a 120GB IDE hard drive. Even with a lot of compression, the drive's contents just don't fit onto that tape, PLUS it takes several hours to try (between the copy+compress, then the write to tape). The consequence of this is that I don't do backup runs as often as I should. So I got a second hard drive and set my PC up to do a filesystem sync from disk to disk (rsync is good!) a couple minutes after I boot, and thus the second disk is a warm spare. And the other issue is that when my tape drive finally dies, it's going to cost me on the order of $1k to replace - with 120GB IDE drives at less than $100 and dropping, I could get ten drives and removabale carriers for that! It's just not worth it for me to continue to invest in tape.
I think there's simply a point in terms of organizational size / backup criticality / cost sensitivity at which tapes start making sense. For low-end folks, I think a bunch of IDE drives are a better choice. For high-end folks, I think tapes remain the best choice. For the middle folks, it's all about deciding which trade-offs to make.