The single best overall bodyweight-only exercise, in my opinion, would be the one-legged squat. It works the major muscle groups of the legs with bodyweight only, also giving a good cardio effect.
You can also do what are called "pistol squats."
This is a one legged squat where you hold your non-working leg out in front of you. That requires great balance and is even more demanding.
I like to do pistols standing on top of a box or Step risers. This allows you to perform the exercise without needing to be quite as flexible. It also means your hip flexors don't have to work as hard to raise the non-working leg.
If you want to make it even more challenging, you can add some weight held out in front of you. This will bring the upper body into the exercise, making it even more challenging.
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