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What's the life expectancy of the typical power supply? >>
That really depends heavily on the manufacturer. I think generic ones are rated at 15,000 hours or so, while quality ones can go up to 50,000 hours. However, those numbers are almost always heavily exaggerated.
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If they go bad, do they simply die and stop working, or can they became faulty and damage the components it's supplying power to? >>
Again, that depends. Sometimes a PSU will just die, and components won't get power, so your rig won't turn on. Other times, the PSU won't supply the correct voltages, and will surge power through components, potentially damaging them. Most good PSUs have protection against these surges so that if they fail they don't destroy your other hardware.
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And are there warning signs that a power supply is failing or about to fail, or will it be obvious like no power? >>
Yet again, it depends

It's dependent on how the PSU dies. Sometimes the fan will fail, causing the PSU to overheat, which makes the internal components burst. That's one sign...if you ever notice the fan in your PSU making weird noises or not going, replace it
immediately. Sometimes there are warning signs, but not very often. If you get a quality PSU (Antec, Sparkle, Topower, PCP&P) then you won't have to worry about anything, as it's extremely unlikely they'll go bad or have problems. I've got rigs from 1994 where I've replaced tons of components in them, but they're still running the same power supply they came with. Good power supplies will probably live about as long as you will
Hope that helps.
J3