This may not be the most elegant solution -- I cloned the original definitions of \footnotemark and \footnotetext and added a closing brace at the appropriate location. (If one wanted to use the optional arguments of \footnotemark/footenotetext, more "cloned" definitions would be needed.)
\documentclass{article}
\makeatletter
\def\quotingfootnotemark{%
\@ifnextchar[\@xfootnotemark
{\stepcounter{footnote}%
\protected@xdef\@thefnmark{\thefootnote)}%
\@footnotemark}}
\def\quotingfootnotetext{%
\@ifnextchar [\@xfootnotenext
{\protected@xdef\@thefnmark{\thempfn)}%
\@footnotetext}}
\makeatother
\begin{document}
\begin{figure}
\centering
\rule{1cm}{1cm}
\caption[A figure]{A figure\quotingfootnotemark}
\end{figure}
\quotingfootnotetext{A quoting footnote.}
Some text.\footnote{A standard footnote.}
Some text.\footnotemark
\footnotetext{A standard footnote produced with \texttt{\textbackslash
footnotemark} and \texttt{\textbackslash footnotetext}.}
\end{document}
\footnotemarkand\footnotetextbut found no other solution. – Mirco Aug 29 '11 at 11:53\footnotemarkquoting? I don't want the closing paranthesis to be put at every footnote. – Mirco Aug 29 '11 at 12:27