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!)
Every automorphism of $S_n$ is inner if $n \neq 6$. 

P.S. That $S_6$ has an `essentially' unique outer automorphism is quite a non-obvious fact.
Have a look at the Strong Law of Small Numbers:


  When two numbers look equal, it ain't necessarily so.