Mine has run constantly for the past 6 months only being turned off once or twice due to power outages. Ive had no slowdowns and zero problems with it.
I'm going to ignore that last post.
It's also good to reboot your computer every few days to clear out the RAM. I personally don't believe it's good for computer to leave it on for weeks at a time.
Sounds similar/linked to thermal stressAcutally, there COULD be a danger if you DON'T leave it running, but the chances are remote. It's called "Chip Creep". When the chips in your computer expand and contract, it tends to losen them in their sockets and they work their way out. these days, most of the chips are Soldered in though, so that's really not a big issue. I just thought i would throw that out there.