It depends on the setup. If there are multiple cops or doctors then it is more likely than not for one to be normal (sane) and the other to be impaired. While some like the naive roles are compleatly useless, others like the insane cop are just as useful as the normal variation if the person figures out he is insane.

You can find info on many roles here
Roles - MafiaWiki

There are some in this page as well, but they are mostly joke roles.
Worst roles ever - MafiaWiki