"Pistols," or one-legged squats using only your body weight, are also excellent for working up knee stability. Since you're holding your weight on one leg and becuase the pistol takes a great deal of work from stabilizing muscles to keep you balanced, you also get a surprisingly decent work-out and some of the full-body effects of squatting. While working up to getting smooth at the pistol, you can cheat by holding on to a doorframe to balance, or the sink, or helping balance or push a little with your opposite foot.
If it takes you a long time to get the pistol right, it's time well spent. It's the perfect exercise for people who can't or won't do squats, getting your core, hams, glutes, thighs, calves, hip flexors, working on your balance a bit, and your flexibility.