|MadSci Network: Computer Science|
It doesn't cost that much to leave it on all the time, depending on local electricity rates. The damage done to a PC by turning it on is quite minimal, but for convenience sake, many folks do leave them on all the time.
The important to do is take advantage of sleep modes, both on your monitor and PC. so when they are "on," they will power themselves down into sleep mode after X minutes of non-use. The annual cost of running a pc is less than $20 on average rates, but can be higher if you don't leverage sleep modes.
Try the links in the MadSci Library for more information on Computer Science.