Barbell squats, when performed correctly and with proper programming will strengthen the tendons, ligaments and muscles around your knees and basically will help you have healthier knees. I had chronic knee pain all my life (from being fat and then from jogging with poor form) until I started squatting.
Thanks, that's what I wanted to hear ;-)
Two more things:
-What are some good, foolproof/simple back exercises?
-I'm utterly useless when it comes to pull ups. What's a good way to approach them when your body weight exceeds your strength?