After years of rolling my ankles, either while playing tennis, soccer, or hiking, I threw in the towel and started wearing braces on both ankles when doing any sport that involves running & cutting. While they don't prevent an ankle roll, they definitely reduce the severity of one.
There were people throwing around allegations that wearing them all the time would weaken your ankles, but there is no evidence to support that theory. Sure, you immobilize your ankles for a few days and the muscles will begin to atrophy, but you're not wearing them 24 hours a day, only when doing exercise that risks an ankle roll.
The only draw back is finding a pair of shoes that are wide enough to accommodate the added girth of the braces. I've found the Cage series and Barricade to be perfect (although I don't like the fit of the Barricades in general). The Gel Res 7s are a close 2nd, but I guess this all depends on the size of your feet.