The contents within a figure environment is treated like any part of the document in terms of typesetting (apart from some length changes). So, you can insert a paragraph break after the first three, which will insert a paragraph break between the image sets. If you want a larger gap, you can insert more vertical space.
Here is a mock-up of what you're after:
\begin{figure}
\centering
\hspace*{\fill}
\subfloat[A gull]{\label{fig:gull}\includegraphics[width=0.3\textwidth]{gull}} \hfill
\subfloat[A tiger]{\label{fig:tiger}\includegraphics[width=0.3\textwidth]{tiger}} \hfill
\subfloat[A mouse]{\label{fig:mouse}\includegraphics[width=0.3\textwidth]{mouse}}
\hspace*{\fill}
\bigskip% or \medskip or \smallskip or \vspace{<len>}
\hspace*{\fill}
\subfloat[An elephant]{\label{fig:elephant}\includegraphics[width=0.3\textwidth]{elephant}} \hfill
\subfloat[A leopard]{\label{fig:leopard}\includegraphics[width=0.3\textwidth]{leopard}} \hfill
\subfloat[A sloth]{\label{fig:sloth}\includegraphics[width=0.3\textwidth]{sloth}}
\hspace*{\fill}
\caption{Pictures of animals}
\label{fig:animals}
\end{figure}
I've inserted \bigskip, although the other listed vertical gap measures would also allow you to tweak the distance.
Using \hspace*{\fill}...\hfill...\hfill...\hspace*{\fill} allows one to distribute the images equally across the text block width. At the moment, you're only occupying 90% of \textwidth (3 images of width .3\textwidth). The aforementioned technique inserts 10% of \textwidth evenly distributed in the 4 spaces around the 3 images. Perhaps you're interested in that, perhaps not.
Note that it is better to put the elephant as far away from the mouse as possible...
\subfloats. – Jake Feb 04 '12 at 03:43