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!)

Mitchell's theorem: A primitive complex reflection group is either the symmetric group $S_n \subseteq GL_{n-1}(\mathbb{C})$ or one of $34$ exceptions.
Definitions: a complex reflection group is a finite subgroup $W$ of $GL_n(\mathbb{C})$ for some $n$, that is generated by reflections. A reflection is an invertible matrix with codimension one fixed space. A complex reflection group $W \subseteq GL_n(\mathbb{C})$ acting on $V=\mathbb{C}^n$ is imprimitive if there is a decomposition $V=V_1 \oplus V_2$ such that for each $w \in W$, and $i=1,2$, $w(V_i) \subseteq V_j$ for some $j$. Otherwise it is primitive.
