Question: The [Whitney graph isomorphism theorem](https://en.wikipedia.org/wiki/Line_graph#Whitney_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](http://en.wikipedia.org/wiki/Classification_of_finite_simple_groups#Statement_of_the_classification_theorem): 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](https://en.wiktionary.org/wiki/sporadically).
> 
> 
> 

(A late thanks to Asaf!)

Answer: 
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.
Polynomial equations of every degree have no general solution in radicals, with the exception of degrees 1, 2, 3 and 4.