Good question. I guess it's a matter of how you define "cure". A psych will tell you that no mental illness can be cured, because they're thinking of it from a physiological point of view. A broken bone can be healed, but from a psych's point of view the brain can't be healed in the same way.

As Sannah points out, though, one can be "cured" of one symptoms whether or not significant physical changes take place in the brain...though there seems to be a lot of new evidence that suggests that such changes do in fact take place. What I mean is that the brain is more malleable than we once thought.

So I guess I take back what I say, with caveats...such as I think it's really really hard for most people to absolutely "cure" themselves.