Make less space between lines on a table

As David Carlisle pointed out at extrarowheight vs arraystretch, \extrarowheight is a length added by the array package to change the default inter-line gap setting between array or tabular lines. It can be positive or negative (though it appears the negative values are limited in how close they can scrunch the lines).

Here is a demonstration showing both negative and positive \extrarowheight:

\documentclass{article}
\usepackage{array}
\begin{document}

\begin {table}[ht]
\begin{center}
  \setlength\extrarowheight{-3pt}
  \begin{tabular}{ccc}
  1 & 2 & 3\\
  4 & 5 & 6\\
  7 & 8 & 9\\
  \end{tabular}
  \caption{My caption}
 \end{center}
\end{table}

\begin {table}[ht]
\begin{center}
  \setlength\extrarowheight{6pt}
  \begin{tabular}{ccc}
  1 & 2 & 3\\
  4 & 5 & 6\\
  7 & 8 & 9\\
  \end{tabular}
  \caption{My caption}
 \end{center}
\end{table}

\end{document}