I use a number of Lacie D2 Quadra drives + OWC Mercury Elite enclosures with WD Caviar Black SATA drives. They have been 100% reliable for many years. (I formerly used Seagate Barracuda drives, but gradually migrated to the Caviar Blacks). In practice, I have 3x backups on separate drives. The drives are only connected during backup operation, otherwise they are disconnected from my Macs, each other and power. I keep one set offsite.
For my more frequent, interim backups, I also use a Lacie D2 Network2 online in my network; I back up email & documents more frequently than other files since they change daily. I use a combination of manual copies via the Finder and automated backups via CarbonCopyCloner depending on what I want to backup at any particular time. I do not use Time Machine or a Time Capsule.
RAID is interesting and useful, but it is not backup. Mirroring only protects you against a single hard drive failure in the Mirror set itself. It does not protect you from software, user or system errors, which are much more frequent than hard drive failures. And in the event the RAID Mirror enclosure itself fails, both drives are likely to be unusable.
My desktop backup system is similar to MartinR's.
For my MBA - I like the idea of wireless backups but don't trust them so I use a lower tech solution. The computer travels daily between home and work so at work I connect it to an external drive which I use for TimeMachine backups. At home I have a drive hidden under the end table next to my comfy chair and the first thing I do when I get home is connect the computer to it. I use DropBox to sync my important data between it and my desktop so the really VIP stuff gets backed up again with my desktop backup routine.