Incidentally, a natural 20 is not always a success, and a natural 1 is not always a failure. Assuming we're talking 3E/3.5 and not 4ail.
Attack rolls do always hit (and threat) on a 20, and miss (there are no fumble rules in core, it should stay this way on pain of the planet being virus-bombed by the holy Inquisition) on a 1.
Saving throws follow this rule as of 3.5, but they originally did not, and it would be better (and more consistent) to ignore this and go back to the 3E way. Basically, in the Deities and Demigods book of 3E, Andy "I'm on crack!" Collins made a feat (or an intrinsic deific power) that lets you succeed even if you roll a 1, as long as your bonus is high enough. Except that was the core rules anyway. Then either because he talked loudly enough about it being a good idea, or because other people read that little ability and made the mistake, it somehow found its way into 3.5
Skill checks and Ability checks are not affected by the magic of 1 and 20. Nor are Level checks, Caster/Manifester/Initiator/Your Mum checks, or whatever.