You can't predict every hard-drive failure. But when a drive goes down because certain hardware components are slowly degrading, then S.M.A.R.T. (Self-Monitoring, Analysis, and Reporting Technology) can help warn you of an impending crash, so you have time to run a last-minute backup. Mac OS X already uses S.M.A.R.T. to track the health of drives, but it only runs a check whenever you use Disk Utility to verify a disk. SMARTReporter is a free, open-source tool that checks the S.M.A.R.T. status of drives hourly (by default, or at any interval you set). SMARTReporter can display a menu bar icon to let you know your drive's status (green or red), and it can also show an alert, send you an e-mail, and even execute an application if it detects a problem. SMARTReporter also supports Growl for notifications, as well as the iOS Growl client Prowl so you can get drive-failure notifications on your iPhone.
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, not FireWire or SCSI), but this app can provide a very helpful warning for many types of failures.