Here is the simple method that vehicle testing stations all over the world use to check a ball joint.
Jack the front wheel up on the side you are going to test. Hold the tyre at the top and bottom.
Pull the top of the tyre and push the bottom of the tyre at the same time.
Then do the opposite.
Do this a few times. There should be no movement at all apart from any movement you may get from the tyre.
Any deflection you get through the wheel means that the ball joint is probably faulty.
Finally, grab the wheel with both hands at the bottom and lift the wheel.
Again you should have no movement at all. (Thanks to Martin for sharing this).
Failed ball joints can cause stiff steering, create nasty noises, cause irregular tyre wear or could allow your wheel and hub to become disconnected from the car causing serious damage. Staying alive is a good reason to check them.
Have a look here.