As far as I could see in the documentation, there's no build-in equivalent to \caption* in the KOMA classes, but KOMA gives you the tools to easily define such a command:
\documentclass{scrartcl}
\makeatletter
\newcommand\WLcaption[1]{%
\renewcommand*{\figureformat}{}
\renewcommand*{\tableformat}{}
\renewcommand*{\captionformat}{}
\addtocounter{\@captype}{-1}
\caption{#1}}
\makeatother
\begin{document}
\begin{figure}
\centering
\rule{3cm}{2cm}
\WLcaption{A test caption without label for a figure}
\end{figure}
\begin{figure}
\centering
\rule{3cm}{2cm}
\caption{A test caption with label for a figure}
\end{figure}
\begin{table}
\centering
\rule{3cm}{2cm}
\WLcaption{A test caption without label for a table}
\end{table}
\begin{table}
\centering
\rule{3cm}{2cm}
\caption{A test caption with label for a table}
\end{table}
\end{document}
\caption*not only suppresses the number; it also suppresses the label ("Figure" or "Table"). – Gonzalo Medina Aug 6 '12 at 19:40