Focusing on one leg at a time not only helps you recognize some of your own imbalances in strength and stability, it can translate into stronger bilateral exercises you already enjoy. Think of it this way; if your left leg is generally weaker than your right leg, the right leg may be taking up extra slack to complete the movement. Over time, this may lead to overuse injuries or muscle imbalances.
Note: Before loading any of these exercises, try using just your bodyweight. You may be surprised at the challenge of simply stabilizing on one leg while moving. Once you feel strong and stable with 3-4 sets of 8-10 repetitions, feel free to add some weight.