  We prove that finite Morse index solutions to the Allen-Cahn equation in
$\R^2$ have {\bf finitely many ends} and {\bf linear energy growth}. The main
tool is a {\bf curvature decay estimate} on level sets of these finite Morse
index solutions, which in turn is reduced to a problem on the uniform second
order regularity of clustering interfaces for the singularly perturbed
Allen-Cahn equation in $\R^n$. Using an indirect blow-up technique, in the
spirit of the classical Colding-Minicozzi theory in minimal surfaces, we show
that the {\bf obstruction} to the uniform second order regularity of clustering
interfaces in $\R^n$ is associated to the existence of nontrivial entire
solutions to a (finite or infinite) {\bf Toda system} in $\R^{n-1}$. For finite
Morse index solutions in $\R^2$, we show that this obstruction does not exist
by using information on stable solutions of the Toda system.
