Making a small modification to a LaTeX environment

\let\oldfigure\figure
\def\figure{\oldfigure\centering}

Another solution which works with the optional arguments.

Fixed.

\let\oldfigure\figure
\let\oldendfigure\endfigure
\def\figure{\begingroup \oldfigure}
\def\endfigure{\centering \oldendfigure \endgroup}

Fixed 2. It does work well with any options and any rules and \par inside.

\makeatletter
\let\oldfigure\figure
\def\figure{\@ifnextchar[\figure@i \figure@ii}
\def\figure@i[#1]{\oldfigure[#1]\centering}
\def\figure@ii{\oldfigure\centering}
\makeatother