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?
5 Answers
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.
1Are 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
1To 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} 2 