There is a school of thought that the most damaging thing for electronics is 'thermal cycling'. Of course running a computer 24/7, the computer never cools down, so it might last a little longer, They used to say hard drives wear out from stopping and starting. I think there's something to that point of view. The HD is the only mechanical part of a computer (well that and the fans) and they run by a whole different set of rules.
But the thing is, computers don't wear out, they go obsolete. You use a computer for 2-3 years on average. Look on Craigslist and you'll see a ton of computers that are still working just fine but nobody wants them because they're leftovers from the GW Bush administration, the Computer Stone Age. (They're not completely useless. They're good for a lot of things. But they're $30 on Craigslist because nobody wants them!)
So if you were to do something that shortened your computer's life by 50%, it would make no difference Long before it died, you would have moved on to a new computer. If never turning off your computer -doubled- its life, what would be the point? Not to mention all that electricity you're burning up year after year.