First, three questions...
 #1: Do you care?
If you threw your computer out of a high rise window, would you miss it? eMails? Photos? Your music library? Bank records, vacation videos, letters, bookmarks, the only portrait of the love of your life....? If you answered 'no' good for you! There _is_ more to life after all. But, if you use a computer at all, you should know that all your data is stored on a fragile device that is certain to fail eventually. Having a backup is only prudent.

 #2: How much data are we talking about?
Gigabytes, terabytes or exebytes? Got a humongous music library? Loads of video? Want to use a MacMini or Apple TV to create a media center (with backup)? Time to look into a RAID array? Twin servers?
For most folks - especially those using notebooks and iMacs - a secondary Firewire drive equal to or larger than capacity of primary volume (hard drive) is sufficient. Why Firewire? Because it's fast (second only to SCSI), and because it will give you the option of startup from a secondary volume. (New Macs may also boot from USB-2, but Firewire is best - why not do it right?)

The drive enclosure pictured here is for a standard 3.5" (full-size) hard drive. It has both FireWire and USB ports, requires a power brick, and cools by convection. Some enclosures have fans, some are stackable, some are made from plastic and others, like this example, are made of aluminum. All have a bridgeboard which converts ATA or SATA to FireWire and/or USB.
Add an appropriate type/capacity hard drive, and you've completed the hardware portion of a backup. (Suggested software is covered below.)
Smaller 2.5" notebook drives also have external Firewire enclosures available for use as portable backup. Their advantage is compact size and the ability to draw power directly from your Mac's Firewire port, eliminating the need for a power brick.

 #3: Is Security a concern?
  • Top Priority, at any cost. You have two choices (basically): Secure, continuous and complete, rotating and redundant, offsite and daily (if not real-time) backup over a secure network - or - hand-carried physical volume rotated thru secure offsite location. Recovery from a total disaster should take no longer than a restart from backup volume/server.
  • Privacy is appreciated: Automated, scheduled onsite backup, password protection if/when necessary. Schedule determined by acceptable loss, job schedule, and/or convenience. Security isn't a big concern. Fair enough.
  • Security is not an issue (workstation, for example), but data loss is always an issue. Daily, weekly or (at least) monthly backup, depending on possible setback weighed against convenience. Any workable plan is better than none.
It has to be dependable (first) and convenient.
If you use a Mac tower, you have extra hard drive bays wired and ready for internal backup drives. This will protect against the primary concern of a drive failure, but it won't protect you from a fire, flood or other disaster that might destroy the entire machine - only offsite backup can do that. On the up side, this backup plan couldn't be any easier or cost effective.

iMacs, Minis and notebooks, of course, have no room for additional internal drives, so an external backup is your only option. If you travel with a notebook, a 2.5" IDE or SATA Firewire-equipped enclosure is your best bet. Small, portable and self-contained, they're easy to pack and use. Otherwise, a desktop unit like the one pictured above (also Firewire) can stay on your desk as a backup volume.

There is also the option of backing up to a server over the internet, if you don't mind an annual or monthly fee and you're okay with sending all your personal info to an unknown location for storage. A MobileMe account (formerly known as dot-Mac) is cost effective and also allows you to synchronize your address book, emails and other files while on the road.

 First half is hardware, second half is software:
Starting with OSX Leopard 10.5, Apple has addressed backup by providing their built-in Time Machine backup utility, providing automation with plenty of options once setup has been completed.

Other backup utilities include the excellent long-time Mac standard, EMC Retrospect, a full-featured utility which does an outstanding  job of copying data even when files may have become corrupted or damaged.
Carbon Copy Cloner (free) is another popular choice.
The program we recommend most is called SuperDuper! from Shirt Pocket. It has a clear and easy interface, is quick and reliable, with an outstanding feature set at a very reasonable price.