You can achieve this using the caption package which gives you access to the \ContinuedFloat float command (to keep the figure number the same) and an additional field to the \caption which when used but left empty prevent the figure to be mentioned in the List of Figures:
\documentclass{article}
\usepackage{graphicx}
\usepackage{caption}
\begin{document}
\begin{figure}[!ht]
\centering
\includegraphics[height=18cm]{pic1}
\caption{caption}
\end{figure}
\begin{figure}[!ht]
\ContinuedFloat
\centering
\includegraphics[height=18cm]{pic2}
\caption[]{caption (continued)}
\end{figure}
\end{document}
If you use the subfig package as well, you can also include the graphics inside a subfloat which would enable you to give each graphic it own caption in addition to the main figure one:
\subfloat[][]{\includegraphics[height=18cm]{pic2}}
this would then use an alpha counter within the figure to differentiate between the parts. The second [] can contain the subfloat caption.