Theorems with an extraordinary exception or a small number of sporadic exceptions The Whitney graph isomorphism theorem gives an example of an extraordinary exception: a very general statement holds except for one very specific case.
Another example is the classification theorem for finite simple groups: a very general statement holds except for very few (26) sporadic cases. 
I am looking for more of this kind of theorems-with-not-so-many-sporadic-exceptions 

(added:) where the exceptions don't come in a row and/or
  in the beginning - but are scattered truly sporadically.

(A late thanks to Asaf!)

Map Color Theorem: For any surface $\Sigma$ with Euler characteristic $c \leq 0$, with the exception of the Klein bottle,
$$\chi(\Sigma) = \frac{1}{2} (7 + \sqrt{49 - 24c}),$$
where $\chi$ is the chromatic number.
