Is it safe to use ankle braces just as prevention, and not as support for a current sprain? I heard that your ankles become adapted to the ankle brace's support and if you were to try and play without them, they would be too weak to support themselves.
I have experienced ankle rolls on each foot, if that makes sense.
Yes, ankle braces have been shown in several large studies of basketball players to preventatively reduce the recurrence of sprains in individuals who have previously sprained their ankles. (a good one is here:
http://www.ncbi.nlm.nih.gov/pubmed?term=21926383) It would be reasonable to assume the same can be said of tennis since the change-of-direction movements in basketball extends to the tennis court.
However, it does not reduce the number of sprains in those who have never sprained their ankle before nor does it reduce the severity of injury if you do sprain your ankle with the brace on.
I do remember reading that bracing prophylactic bracing does not cause weaker ankles in persons who consistently wore them in sports training although I can't remember the actual study that measured this. The way ankle bracing is postulated to reduce sprains is by increasing proprioceptive feedback rather than actual mechanical support. What this means is that, when you invert or evert your ankle with a brace on, the brace pulls on your skin and muscles to send extra signals to your spinal chord and brain about what position your ankle is in. This way, you will reflexively correct your foot position back to neutral before it rolls too far and sprains the ligament. While it does add some mechanical support, it is insufficient to prevent the severity of a sprain in high velocity in sports.
Balance/wobble-board training improves proprioception as well by retraining the nerves to relearn your foot positioning and fire faster. The reason why people typically resprain their ankles is because the first sprain stretched and damaged these nerves in the lower leg.
Short story: If you've sprained your ankle before and want to reduce the chances of future sprains as much as possible, do lots of balance work AND wear a brace. Shoes do nothing.