I bought a new computer in 1999 (Dell 450MHz and a big-at-the-time 28 gig drive), ran it 24 hours a day, and the hard drive only died a year or so ago. It even had the original Windows 98 installation. Reinstalling Windows is almost always a sledgehammer approach to problems.
And yes, always set up the power options to turn off the monitor and stuff, because if it's sitting there for more than an hour you're likely not in front of it and the monitor might as well turn off.
But I think modern computers are reliable enough that it doesn't make any difference. You'll save electricity by turning it off. On the other hand, if the bootup time bugs you, just leave it on. Reboot once or twice a week, or whenever it seems slow or wonky, to clear out Microsoft's memory leaks and you'll be fine. I've run Ubuntu, but not for weeks and weeks of regular usage at a time, so I don't know if it has any such problems. I get the impression it doesn't.
And like someone else said, once a year open the case and blow out the dust. Dust buildup causes lowered airflow and more heat buildup, and if there's ever really high humidity the dust could absorb water from the air and become conductive, a bad thing.
ETA: Whether or not you run your computer all the time, you might want to "give away" extra CPU cycles to some distributed computing project or other. I do this one:
http://www.mersenne.org/
but not for the money, the chance of winning something is pretty low. Here's one of the biggest for medical research:
http://folding.stanford.edu/
And then there's the ever-popular one to find the elusive "LGM" signal:
http://setiathome.berkeley.edu/