Two statements next to curly brace in an equation

How can I write an equation with one curly brace ({), and on the right-hand side next to the curly, two statements in two different lines?

You can try the cases env in amsmath.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{equation}
  f(x)=\begin{cases}
    1, & \text{if $x<0$}.\\
    0, & \text{otherwise}.
  \end{cases}
\end{equation}

\end{document}

That can be achieve in plain LaTeX without any specific package.

\documentclass{article}
\begin{document}
This is your only binary choices
\begin{math}
  \left\{
    \begin{array}{l}
      0\\
      1
    \end{array}
  \right.
\end{math}
\end{document}

This code produces something which looks what you seems to need.

The same example as in the @Tombart can be obtained with similar code.

\documentclass{article}

\begin{document}

\begin{math}
  f(x)=\left\{
    \begin{array}{ll}
      1, & \mbox{if $x<0$}.\\
      0, & \mbox{otherwise}.
    \end{array}
  \right.
\end{math}

\end{document}

This code produces very similar results.

Are you looking for

\begin{cases}
  math text
\end{cases}

It wasn't very clear from the description. But may be this is what you are looking for http://en.wikipedia.org/wiki/Help:Displaying_a_formula#Continuation_and_cases

To answer also to the comment by @MLT, there is an alternative to the standard cases environment, not too sophisticated really, with both lines numbered. This code:

\documentclass{article}
\usepackage{amsmath}
\usepackage{cases}

\begin{document}

\begin{numcases}{f(x)=}
  1, & if $x<0$\\
  0, & otherwise
\end{numcases}

\end{document}

produces

Notice that here, math must be delimited by \(...\) or $...$, at least on the right of & in each line (reference).

Or this:

f(x)=\begin{cases}
0, & -\pi\leqslant x <0\\
\pi, & 0 \leqslant x \leqslant +\pi
\end{cases}