The most important decision regarding backups is the choice of backup medium. You need to consider cost, reliability, speed, availability, and usability.
Cost is important, since you should preferably have several times more backup storage than what you need for the data. A cheap medium is usually a must.
Reliability is extremely important, since a broken backup can make a grown man cry. A backup medium must be able to hold data without corruption for years. The way you use the medium affects it reliability as a backup medium. A hard disk is typically very reliable, but as a backup medium it is not very reliable, if it is in the same computer as the disk you are backing up.
Speed is usually not very important, if backups can be done without interaction. It doesn't matter if a backup takes two hours, as long as it needs no supervision. On the other hand, if the backup can't be done when the computer would otherwise be idle, then speed is an issue.
Availability is obviously necessary, since you can't use a backup medium if it doesn't exist. Less obvious is the need for the medium to be available even in the future, and on computers other than your own. Otherwise you may not be able to restore your backups after a disaster.
Usability is a large factor in how often backups are made. The easier it is to make backups, the better. A backup medium mustn't be hard or boring to use.
The typical alternatives are floppies and tapes. Floppies are very cheap, fairly reliable, not very fast, very available, but not very usable for large amounts of data. Tapes are cheap to somewhat expensive, fairly reliable, fairly fast, quite available, and, depending on the size of the tape, quite comfortable.
There are other alternatives. They are usually not very good on availability, but if that is not a problem, they can be better in other ways. For example, magneto-optical disks can have good sides of both floppies (they're random access, making restoration of a single file quick) and tapes (contain a lot of data).