Large braces for specifying values of variables by condition

The cases environment from amsmath does the trick.

\documentclass{article}
\usepackage{amsmath}

\begin{document}
  \begin{equation}
    X=
    \begin{cases}
      0, & \text{if}\ a=1 \\
      1, & \text{otherwise}
    \end{cases}
  \end{equation}
\end{document}

Another method, which is especially helpful if one needs to have more control over the items alignment, is the array construct.

\documentclass{article}
\usepackage{amsmath}    
\begin{document}

\begin{equation}
  X=\left\{
  \begin{array}{@{}ll@{}}
    0, & \text{if}\ a=1 \\
    1, & \text{otherwise}
  \end{array}\right.
\end{equation} 

\end{document}

Instead of ll, one may choose cc, rr, rl, etc. Besides, all the array capabilities can be applied here (\arraycolsep, \arraystretch, \extrarowheight by loading the array package, etc).

One more alternative could be using the aligned environment and adding the pseudo-parenthesis ., which can be used to terminate an opening parenthesis {.

\documentclass{article}
\usepackage{amsmath}    
\begin{document}

\begin{equation}
  X = \left \{
  \begin{aligned}
    &0, && \text{if}\ a=1 \\
    &1, && \text{otherwise}
  \end{aligned} \right.
\end{equation} 

\end{document}

x = \begin{cases}
  0, & \text{if } a = 1, \\
  1, & \text{otherwise}.
\end{cases}

amsmath is needed for \text.