How likely is it that an Xbox 360 hard drive will die, and are there any early warning signs or indicators?
Solution 1:
It is almost impossible to predict when a hard drive will go bad. I've had desktop hard drives that went bad after 9 months. I've also had some that are still working after 10 years (and I still have a Tandy even with a working hard drive!)
Sometimes when a hard drive begins to fail it will perform very poorly and/or exhibit the "click of death." When either of these things happen(especially the click) it is time to buy another one and stop using the hard drive until you are ready to back it up. Note, the few hard drives I've had that failed, failed suddenly without any slow downs. They just one day didn't work.
Other than that, to ensure a long hard drive life is not to bang it or other rough hard movements. Also, store it somewhere between 70-100 degrees Fahrenheit and run it in such a temperature range. Also, make sure it isn't in an overly dusty environment.
Solution 2:
Provided you take good care of it you shouldn't see it fail for a very long time.
In around 2 years working at a games store the only time we ever saw a hard drive come back was because someone had been rough with it or pulled the power out at an awkward moment.
If you're concerned it might be useful to back up some save games to a memory card.
Solution 3:
Unless there are early signs (which are harder to see with a 360 vs. a desktop or laptop), the only real option is preemptive replacement. I haven't experienced this yet, as my 360 is only a year and a half old, but I suspect that many who would have have already upgraded their drives because of space issues.