What sort of problems do see crop up?
Motherboard dead. Push power button, nothing or next to nothing happens (i.e. fans might spurt or the power light sort of come on). Replace the motherboard and it is just like new.
These are computers that are well over a year old by the way. Sleep mode doesn't kill them overnight. I think it must have something to do with the memory still being powered but other equipment being off. Perhaps that stresses the equipment on the microscopic level and, given enough time, causes permanent damage due to irregular heating patterns across the motherboard. I am not certain on this but there is definitely a trend present. Hibernation is better than sleep mode in terms of hardware preservation but it also involves complex operations on the hardware's behalf. I would trust hibernation more than sleep and turning it off trumps everything; however, if you're going to turn an electronic device all the way off, it shouldn't be turned back on for a good half an hour.
And remember, all PC hardware is tested under the assumption that it will have to power up and down repeatedly throughout its life span. Yes, it causes some wear but not enough to justify leaving it on all the time you aren't in front of it. Yes, the components are stressed to a high degree in the few milliseconds after the power starts flowing but they are designed to take that abuse. And yes, if there is going to be a major component failure, it is likely to occur in the that brief period; however, it is going to fail no matter what (rather, it already failed--just hasn't exposed itself). By not turning it off, you are merely prolonging the inevitable. XD
Motherboard failures on boot are preferrable to motherboard failures while in use because there is a very good chance that the data on the hard drive will remain uncorrupted. If the component is pushed so far that it causes instability, any and every file that is currently being written to the hard drive has a high risk of being damaged. Not to mention, a much higher risk of taking other computer components with it when it goes.
In the end, convserving power and reducing heat production (furnaces are more efficient in the winter/air conditioners fight it in the summer) is better than thriving off the long odds it's going to fail any time you turn it on.
My computer has seen no less than 900 on/off cycles and its still going strong.
Ack, that turned into a chapter from a book.
