For as long as I have been running (since 1997), I've had a problem with spraining my ankles. In both track and XC, I kept spraining my ankles. I went to PT, rested, did strengthening exercises, did a daily regimen of balance exercises (some a balance board), tried to keep it on the 'crete rather than on trails, and so on. Finally, in 2001, I had my left ankle reconstructed, and decided to quit running.
I started running again in 2010, and after about six months, sprained my ankle again. I run about 50-60mpw in the Asics GT series, in the Brooks Trance, and race 5K and up in whatever flat I have lying around.
Any thoughts on what type of running shoe (or features of a running shoe) would best decrease the likelihood of ankle sprains?