There are specific exercised that concentrate on balance and develop proprioception. This means having the muscle reflexes tuned to respond to an uneven position and stabilize the ankle. One such training method is running on an uneven surface, such as a on a beach or a trail instead of the road. This has shown to decrease ankle sprains in soccer players. Another way is balancing on one leg, as you get better you can increase the difficulty by closing your eyes, by making the surface unstable, such as a pillow or a wobble board and finally by trying to complete another task at the same time such as handling a ball.
Ligaments protect the ankle joint, but are assisted by the muscles and tendons. Although we cannot strengthen the ligaments, we can strengthen the muscles with specific ankle exercises. Many of these exercises are difficult with standard weights and training machines, elastic bands are quite helpful.
Stretching can be beneficial, but don’t count on stretching just before your sport. Stretching contributes to flexibility, but to be truly effective it must be part of your regular training routine.
One thing that can help just before a sport is proper warm up. Getting the muscles ready to perform by warming up with sport specific exercises have been shown to reduce injury.
In certain sports are at high risk for ankle sprains. Basketball and football are the first to come to mind. Many players use taping to prevent injury while other use a lace up ankle brace. The evidence is mixed for preventative taping but some scientific studies indicate that bracing may be helpful in high-risk sports. One caveat though, bracing does not replace the changes to training mentioned above, they are the most important element to prevent ankle injuries while enjoying your sport.