How to put large figure caption on separate page from the figure

The ccaption package provides continued captions via \contcaption:

\documentclass{article}
\usepackage{graphicx}% http://ctan.org/pkg/graphicx
\usepackage{lipsum}% http://ctan.org/pkg/lipsum
\usepackage{ccaption}% http://ctan.org/pkg/ccaption
\begin{document}
\section{A section}
\lipsum[1-10]
\begin{figure}[t]
  \centering
  \fbox{\includegraphics[height=.6\textheight]{tiger}}
  \caption{(Continued on the following page.)}% First caption
  \label{fig:tiger}
\end{figure}
\begin{figure}[t]
  \contcaption{\lipsum[1-2]}% Continued caption
\end{figure}
\lipsum[11-15]
\end{document}

It effective does what you suggest:

\addtocounter{\@captype}{\m@ne}% Add -1 to float counter
\refstepcounter{\@captype}% Step and mark float counter
% ...and the rest

Note though that continuous captions could cause problems when used in conjunction with hyperref.

The easiest method I came up with is to break up the caption into a second figure and use the \addtocounter command to make sure the caption has the same figure number

\begin{figure} [b!]
  \centering 
  \includegraphics[width=\textwidth]{figure.pdf}
  \caption{(Caption next page.)}
  \label{figurelabel}
\end{figure}
\addtocounter{figure}{-1}
\begin{figure} [t!]
  \caption{(Previous page.) Caption goes here.}%missing
\end{figure}

Notes:

• I included "(Caption next page.)" as the \caption{} attached to the actual figure and prefixed the true caption with "(Previous page.)".

• I used the [b!] and [t!] options for figure and caption, respectively. This isn't necessary, but it makes sure they are as close as possible to each other within the document.

Drawbacks:

• LaTeX will not automatically make sure that the caption is on the page immediately after the figure.

• The caption will not be "reattached" to the figure if the caption is made short enough to fit on the same page (which would be nice LaTeX best practices).

• As Yiannis Lazarides notes, the figures would ideally appear on odd pages and captions would appear after them on even pages, so you can always see both at the same time. This hack doesn't ensure that happens.

As Thorsten already mentioned, the fltpage package might be useful here:

\documentclass{article}
\usepackage[demo]{graphicx}
\usepackage[CaptionAfterwards]{fltpage}
\usepackage{lipsum}

\begin{document}
\begin{FPfigure}
  \centering
  \includegraphics[width=\textwidth,height=\textheight]{figure.pdf}
  \caption{Caption goes here.}
  \label{figurelabel}
\end{FPfigure}
\lipsum
\end{document}

(Please note that currently the fltpage package does not work well with hyperref, at least if you don't use the caption package additionally.)