\frontmatter and \mainmatter will suffice for different styles of page numbering, but not for roman numbering of introductory tables (which are quite uncommon). Assuming you have only one frontmatter chapter that includes tables, the following should do the trick:
\documentclass{book}
\begin{document}
\frontmatter
\begingroup
\renewcommand{\thetable}{\Roman{table}}
\chapter{foo}
Some text.
\begin{table}
\caption{bla}
\end{table}
\endgroup
\mainmatter
\chapter{bar}
Some text.
\begin{table}
\caption{blubb}
\end{table}
\end{document}
For report and similar classes, replace \frontmatter with \pagenumbering{Roman} and \mainmatter with \cleardoublepage\pagenumbering{arabic}.
scrbook. – Gonzalo Medina Aug 16 '11 at 00:01memoir, too. – Brent.Longborough Feb 10 '12 at 22:53