I went to control panel and I set it so that whenever I press the physical power button on my tower, it puts the computer to sleep. My friend said that this will eventually damage my computer, but I don't believe him. What do you guys think? Also does this also apply if I set the power button to shut down the computer? To hibernate? etc. Thanks for your thoughts!
		
		
	 
Your friend doesn't know what he's talking about.  As others have mentioned, there is a world of difference between tapping the power button and holding it down for several seconds.
Just tapping the power button doesn't do anything to the hardware, it just sends a signal to the OS that the button was pressed.  Tapping the power button is absolutely no different than clicking the Sleep, Shutdown, Hibernate, or whatever in Windows.
Holding it down so that the system powers down hard can potentially lead to data corruption if you were in the middle of something.  Even that is rare in the age of journaled file systems though.