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!)

How about the Big Picard theorem? http://en.wikipedia.org/wiki/Picard_theorem
If a function $f:\mathbb{C}\to \mathbb{C}$ is analytic and has an essential singularity at $z_0\in \mathbb{C}$, then in any open set containing $z_0$, $f(z)$ takes on all possible complex values, with at most one possible exception, infinitely often.
