I think two important characteristics are 

 - The importance of the theorem itself 
 - The extent of connections within the subject

These two are not, of course, mutually exclusive!

This book is a recent discussion of mathematical style which has 99 proofs.  A really great read.

    @BOOK{Ording2019,
      title =     {99 Variations on a Proof},
      author =    {Ording, P.},
      publisher = {Princeton University Press},
      address =   {Princeton and Oxford},
      year =      {2019},
      isbn =      {9780691158839},
    }

and this book collects together proofs of $\sqrt{2}$ is irrational.

    @BOOK{Duchene2010,
      author =       {Duch\^{e}ne, L. and LeBlanc, A.},
      title =        {Rationnel mon Q: 65 exercices de styles},
      publisher =    {Hermann},
      year =         {2010},
    }