Geez Thom, that's a loaded question.
If you mean "technologically" how long should a compluter last, the answer is about three days. If you order the latest-greatest it will be outdated by the time it arrives.
If, however, you mean "mechanically" (for lack of a better term), I have one sitting beside me that is getting close to 15 years old and it just keeps on humming (but I think the hum is the fan

).
You can run diagnostics on it to make sure there are no hardware errors anywhere but other than that, it is anybody's guess as to how long it will last. As long as you maintain a system (keep it on a protected power supply, clean the vents regularly, run hardware diags, keep the OS updated, etc), it should last quite a while.