You can't predict every hard-drive failure. But when a drive goes down because certain hardware components are slowly degrading, then Self-Monitoring Analysis and Reporting Technology, aka S.M.A.R.T., can help warn you of an impending crash so you have time to run a backup.
Mac OS X already uses S.M.A.R.T. to track the health of drives, but it only runs whenever you use Disk Utility to verify a disk. SMARTReporter is an open-source tool that checks the S.M.A.R.T. status of drives hourly, or at any interval you set. It can display a green or red menubar icon to let you know your drive's status, and it can also show an alert, send you an e-mail, and even execute an application if it detects a problem.
Because of the limitations of S.M.A.R.T., SMARTReporter won't catch every impending failure--and unfortunately, it is also limited by OS X to checking ATA, SATA, and eSATA drives--there's no Firewire or SCSI support yet.