Separate labels in cases

You can use numcases from the cases package if you want each case labelled as a separate equation. There is also the subnumcases environment which gives you an alternative labelling:

\documentclass[preview]{standalone}
\usepackage{amsmath}
\usepackage{cases}
\begin{document}
\begin{numcases}{f(x)=}
   1 & $x\geq0$ \label{positive}
   \\
   0 & $x<0$ \label{negative}
\end{numcases}

See the second case \ref{negative} or the first \ref{positive}

\begin{subnumcases}{f(x)=}
   1 & $x\geq0$ \label{positive-subnum}
   \\
   0 & $x<0$ \label{negative-subnum}
\end{subnumcases}

See the second case \ref{negative-subnum} or the first \ref{positive-subnum}
\end{document}

Using only the amsmath package and no additional packages, it is possible with some box manipulation:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\begin{document}
\newsavebox{\mycases}% Store case "title" and brace
\begin{align}
  \sbox{\mycases}{$\displaystyle f(x)=\left\{\begin{array}{@{}c@{}}\vphantom{1\ x\geq0}\\\vphantom{0\ x<0}\end{array}\right.\kern-\nulldelimiterspace$}
  \raisebox{-.5\ht\mycases}[0pt][0pt]{\usebox{\mycases}}1 \quad x\geq0\label{positive} \\
     0 \quad x<0\label{negative}
\end{align}
\end{document}

You can do this by the empheq package from the mh bundle.

\documentclass[11pt]{article}
\usepackage[T1]{fontenc}
\usepackage{empheq}   % loads »mathtools«, which in turn loads »amsmath«

\begin{document}
  \begin{empheq}[left={f(x)=\empheqlbrace}]{align}
    1 &\quad x\geq0\label{positive}\\
    0 &\quad x<0\label{negative}
  \end{empheq}
\end{document}