Um....no they don't need to be plugged in. Just make sure you 'safely remove'/'eject '(depending on your system) the disk before disconnecting from the computer and if it has a power switch, turn it off. I usually keep my Maxtor One Touch II 300GB drive unplugged and off for safety reasons.

I personally have two maxtors (one quite old) and both serve me very well. I'm transitioning to internal drives in an eSATA enclosure, however, to save money for backups. External drives do come at a premium.