Does it use more energy to turn my computer on and off everyday, or leaving it running for a few days?

I am responding to someone elses comments to this question as they were talking about cars. No cars do not use more fuel to start or shut down; That is not the purpose of leaving a car running, The purpose to leave a car running is in two reasons. First, heating and cooling of the heads, especially with the aluminum heads cause them to warp and eventually crack, so leaving your car running instead of shutting it down for short periods is better for the life of your car. Second, oil eases back down into the oil pan when a car is shut down, this leaves little oil in the top of the engine, so there is more friction when it starts up and for the first couple of minutes this friction can damage parts and gradually wear them out. So again, shutting down the engine for short periods can again wear on the engine shortening the engine life;.

Any running electrical item left running will cost you money. Turning a PC on and off for a length of time once a day, will help to reduce your electricity bill. However, if you live in a high humidity area, such as me, it is not practical to turn off a PC for fear of the components rusting. So, I make sure that the screen is turned off whenever I leave the PC. This, definitely saves energy costs and gives the plasma screen a chance to cool down!