The rate of twist (rifling pitch) needed to stabilize a given bullet depends on its length (if of conventional materials), and to some extent, shape, as well as velocity, though to a lesser extent. The basic rule is that you should use a pitch rate which will stabilize the longest (and usually, heaviest) bullet you intend to use in a given caliber, since understabilized bullets (spun at too low RPM) will not maintain the proper point-first attitude and are wildly inaccurate, while overstabilized bullets (spun faster than absolutely necessary to stabilize them) do not suffer from inaccuracy to any real extent. Usually a pitch rate is chosen to give a stability factor of 1.2 or greater (that is, 1.2 times the theoretical RPM necessary for bullet stabilization) - this helps compensate for bullets which are not 'perfect' in any way (usually having the center of mass off the center of rotation due to imperfect shape or a jacket and core not perfectly concentric with each other).
There are several formulae used to calculate the theoretical pitch needed for a given bullet - the Greenhill is a good one for most common sporting uses.