Hello,
I ran a bbs from 1986-1997, the computer ran 24/7. I had to replace the power supply fan a number of times and I had a hard drive that would not spin up on its own if I did turn it off but aside from that, the mother board, memory and all the rest of the parts lasted. I had a hard drive fail with bad sectors after 5 years of use, but that is typical for the drives made in the mid 80's.
It cost me an extra $20 or so a month to run it. Once the internet came along and local boards were no longer needed, I took it down but I still run 2 computers 24/7 now and have been since I took the bbs down. No problems at all, I do have everything running on a big APC. I have had modems die over the years from spikes, but never the computer. I work in the IT field for an insurance company,(500 users) we use mostly compaq deskpros and have video cards die all the time on the users machines, never have any problems with the servers. I would leave them on if it were up to me and just turn off the monitors. But then, we turn off the computer and leave all the lights on...go figure.