Can pilots turn off a plane's transponder?

The aircraft transponder broadcasts a signal every 1 - 15 minutes.  This signal allows the aircraft to be tracked.

Can a pilot turn off their plane's transponder?  For aircraft flying within the FAA airspace, most of the time they are not suppose to.

To dig deep into the law, you can visit Cornell Law School page dedicated to this topic..

The Aircraft Owners and Pilots Association has also written this up.

And the FAA has also published its rules.