Force line break inside a \lim argument in align environment

Use substack to specify the two variables.

As egreg pointed out you can also use subarry and the last two solutions provided use this. The last one also account for the fact that the a and b don't take up the same amount of space, and create a box the width of an x and centers the a and b within that amount of space.

Also, in this case it is better to use \to instead of \rightarrow as that better represents the mathematical sense here.

\documentclass{article}
\usepackage{amsmath}

\begin{document}
\newcommand*{\AlignChar}[1]{\makebox[1ex][c]{\ensuremath{\scriptstyle#1}}}%
\begin{align}
 \lim _{\substack{a \to -\infty \\ b \to \infty}} =
 \lim _{\begin{subarray}{l} a \to -\infty \\ b \to \infty \end{subarray}} =
 \lim _{\begin{subarray}{l} \AlignChar{a}  \to -\infty \\ \AlignChar{b} \to \infty \end{subarray}}
 \end{align}
\end{document}

As per egreg's comments, you could also write:

\newcommand*{\AlignChar}[1]{\makebox[1ex][c]{$\scriptstyle#1$}}%

which would make that macro easier to read, but my personal preference is to use \ensuremath as that to me explicitly captures the fact that it can be used in mode. In this case, the reason that $...$ is ok is that \makebox enters text mode so you can use $..$ or \ensuremath inside it.

Here is a, perhaps less attractive, alternative to stacking limits to operators by using \mathop:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\begin{document}
\begin{align}
f & = \mathop{\lim_{a\rightarrow-\infty}}_{b\rightarrow\infty}
\end{align}
\end{document}​