Yes it is required by law to have your front license plate screwed on the front of your car and yes, i know the car looks way better w/o that fat license plate that blocks the radiator.
OH yeah if you live in LA cops might give you a fix it ticket especially becuase there are cameras all over the place now and it would be pointless for them to get a snapshot of a car running a red light w/o a license to identify the driver.
*** IMPORTANT ***
Never ever put anything around your dashboard on your passenger side becuase when the air bag pops up it might cause some serious damage. If you want to put your license plate on your dash keep it on the driver side.
Well it's required here in IL but I'm almost certain it is a state to state law. Also, if you really want to drive without one, one of my friends took his off, smashed it up a bit, and keeps it in his trunk. When he got pulled over he said someone clipped it in a parking lot and it came off. He didn't get a ticket. I'm not certain that is would work for everyone but it's an idea.