While a figure environment is intended for images and graphics, it is not limited to that, so there is nothing wrong with having a tabular within a figure environment. (Also, as egreg mentioned, an \includegraphics is by no means limited to being within a figure.)
Therefore, you can use standard tabular to lay out your images. An example is below, where I also used the adjustbox package to vertically center the images, as in e.g. https://tex.stackexchange.com/a/46390/586
(The image used is from the mwe package, so if that is installed the code should compile directly.)
\documentclass{article}
\usepackage{graphicx}
\usepackage{adjustbox}
\newcommand\animage{\adjustbox{valign=m,vspace=1pt}{\includegraphics[width=.2\linewidth]{example-image}}}
\begin{document}
\begin{figure}
\centering
\begin{tabular}{cccc}
& Column 1 & Column 2 & Column 3 \\
Row 1 & \animage & \animage & \animage \\
Row 2 & \animage & \animage & \animage \\
Row 3 & \animage & \animage & \animage
\end{tabular}
\caption{Figures}
\end{figure}
\end{document}

\includegraphicsto be in afigureenvironment. – egreg May 26 '13 at 22:20