One of the most important things you can do to strengthen and stabilize the knee is to condition the proprioceptive system. One-legged balance is a great place to start, but you might want to learn the ‘short foot‘ beforehand.
Proprioception is a major part of our balance mechanism, and so conditioning it will improve your ability to cut, turn, jump and land without one part of your body going one way, while another goes the other way. Proprioceptive training is good prevention, period (and good rehab too!).