The cases environment of the amsmath package uses array with the column specification @{}l@{\quad}l@{}. Thus \multicolumn will work, e.g.:
\multicolumn{1}{@{}r@{\quad}}{...}
The alignment can also be influenced by \hfil and \hfill, because array or tabular are using \hfil to align and justify their column types l, c, and r.
\hfill 0 % puts 0 to the right
The following example shows the different methods:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
\begin{cases}
\mbox{left/default} & \mbox{left/default} \\
\multicolumn{1}{@{}l@{\quad}}{\mbox{left}} &
\multicolumn{1}{@{}l@{}} {\mbox{left}} \\
%
\hfil \mbox{center} & \hfil \mbox{center} \\
\multicolumn{1}{@{}c@{\quad}}{\mbox{center}} &
\multicolumn{1}{@{}c@{}} {\mbox{center}} \\
%
\hfill \mbox{right} & \hfill \mbox{right} \\
\multicolumn{1}{@{}r@{\quad}}{\mbox{right}} &
\multicolumn{1}{@{}r@{}} {\mbox{right}} \\
%
\multicolumn{1}{@{}p{10em}@{\quad}}{Column type p \dotfill\newline with two lines \hrulefill} &
\multicolumn{1}{@{}p{10em}@{}} {Column type p \dotfill\newline with two lines \hrulefill} \\
\end{cases}
\]
\end{document}

Applied to the case of the OP:
\documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator{\sgn}{sgn}
\begin{document}
\[
\sgn(x)=
\begin{cases}
-1 & \mbox{za podmínky } x>0\\
\hfill 0 & \mbox{za podmínky } x=0\\
\hfill 1 & \mbox{za podmínky } x>0
\end{cases}
\]
\end{document}

\phantom{-}in front of the0and1– dustin Jul 19 '13 at 23:04\DeclareMathOperator{\sgn}{sgn}at the preamble such that you can use\sgn(x)instead ofsgn(x). – Francis Jul 19 '13 at 23:46\[…\]preferable to$$? – Werner Jul 20 '13 at 01:02