PushButton as LED Switch (does not work)
Based on your response to my comment, it sounds like you have a floating input.  When the button is NOT pressed, the pin isn't connected to ground or 5V so it is floating and picking up whatever stray electrical signals happen to be bouncing around the room.

The easiest way to handle buttons on an Arduino is to wire them between the pin and ground.  Then in the code you use INPUT_PULLUP instead of INPUT for the pinMode call.  Once you've done that then the pin will reliably read HIGH when the button is NOT pushed and will read LOW when the button IS pushed.  Note that this is backwards of how newbies tend to think, but is really the more common way to handle a button.