documentclass{article}

usepackage[pdftex]{graphicx}
usepackage{hyperref}

graphicspath{{./Figures/}}

begin{document}

begin{figure}
includegraphics{NodesEdgesExample2.pdf}
caption{
Paragraph 1.

Paragraph 2.

Paragraph 3.
}
label{fig:AltNavigationConcept}
end{figure}

end{document}

documentclass{article}

begin{document}

listoffigures

section{foo}

begin{figure}[!ht]
centering
rule{1cm}{1cm}
caption[LoF entry]{The first paragraph of a figure's caption.

And the second.}
end{figure}

end{document}

documentclass{article}
usepackage[demo]{graphicx}
usepackage{caption}
usepackage{lipsum}
begin{document}
captionsetup{margin={15pt},parskip=10pt,format=hang,indention=-.8cm}
begin{figure}[h]
centering
includegraphics[width=textwidth]{myfigure}
caption[my caption]{lipsum[1-2]}
end{figure}
This is regular text. lipsum[1]
end{document}