I guess you can use the xcolor package as explained here, but instead of set up alternate table row colors, force to color odd and even rows using the same color:
\usepackage[table]{xcolor}
\definecolor{lightgray}{gray}{0.9}
\rowcolors{1}{gray}{gray}
Here is you have a full working example:
\documentclass[11pt]{article}
\usepackage[table]{xcolor}
\definecolor{lightgray}{gray}{0.9}
\begin{document}
\begin{table}[ht]
\caption{default}
\begin{center}
\rowcolors{1}{lightgray}{lightgray}
\begin{tabular}{r|rrrrr}
\hline
& 1 & 2 & 3 & 4 & 5 \\
\hline
1 & 2.36 & 1.08 & -0.49 & -0.82 & -0.65 \\
2 & -0.68 & -1.13 & -0.42 & -0.72 & 1.51 \\
3 & -1.00 & 0.02 & -0.54 & 0.31 & 1.28 \\
4 & -0.99 & -0.54 & 0.97 & -1.12 & 0.59 \\
5 & -2.35 & -0.29 & -0.53 & 0.30 & -0.30 \\
6 & -0.10 & 0.06 & -0.85 & 0.10 & -0.60 \\
7 & 1.28 & -0.46 & 1.33 & -0.66 & -1.80 \\
8 & 0.80 & 0.46 & 1.37 & 1.73 & 1.93 \\
9 & -0.75 & 0.28 & 0.51 & 0.19 & 0.58 \\
10 & -1.64 & -0.12 & -1.17 & -0.10 & -0.04 \\
\hline
\end{tabular}
\end{center}
\end{table}
\end{document}
And the result:

EDIT: Following Mico's comment, there are two limitations:
- The space around lines created by the
booktabs package's \toprule,
\midrule, \cmidrule, and \bottomrule commands and
- Any intercolumn whitespace. E.g., if one specifies
@{\extracolsep{\fill}} in the tabular* environment's second argument
-- to force the overall width of the table to be equal to the environment's width argument (usually, but not necessarily,
\textwidth) -- the extra intercolumn whitespace
won't be affected by
the \rowcolor statement.