Here are a few that I do:
Burpees/Jump Thrusts: These were my kryptonite during team sports. We did sets of 20 of these puppies, and the first time I ever did them, it felt like I was dying after five. These are good for cardio, leg strength, balance, arm strength, and core strength. They're a full body workout in one exercise, essentially. Or, at least that's what my basketball coach told me.
Step One: Start out in a standing position.
Step Two: Go down into a squatting position, as seen in the picture.
Step Three: From the squatting position, jump back with your feet so that you are in a push-up position.
Step Four: Jump forward with your feet so that you end back in a squatting position.
Step Five: From the squatting position, jump straight up, as high as you can / as high as you can stand to jump.
Repeat as many times as you feel comfortable with. I'd recommend no less than ten reps on this one.
Leg Lifts:
These are painful. I'm not going to lie. They sound fairly innocent in theory, but your legs and abs will hate you after just a couple of reps. Even when I was in the best shape of my life, having to do thirty of these on the last day of conditioning made me feel like I was dying.
Step One: Lay down on your back on the floor or on a mat. Your arms can be behind your head, out to the side, crossed over your chest...whatever is most comfortable.
Step Two: Slowly, keeping your legs straight and together, raise your legs as close to a ninety degree angle as you can without bending your knees or pulling them apart.
Step Three: Slowly lower your legs so they almost touch the ground, still keeping them completely straight. Do NOT allow them to touch the floor.
Repeat until you can do no more. I'd say, again, at least ten would be ideal.
Squats:
These are an essential, really. Great for toning leg muscle. Add hand weights for increased resistance.
Step One: Begin by standing with your feet shoulder width apart.
Step Two: Bend your knees, lowering your body (feet planted!) like you were sitting in a chair. Hold for a second or so.
Step Three: Still keeping your feet planted, raise straight back up into the starting position.
Go for at least thirty reps of these, as they're really not that bad.
These three are absolutely necessary for me. Push-ups are definitely another good body weight exercise, as are pull-ups. Once you've mastered those, you can find more advanced push-ups/pull-ups to work on to further increase your strength.