The following code compiles and acts as you would expect:
\documentclass[12pt]{report}
%\usepackage{hyperref}
\usepackage{subfig}
\begin{document}
\begin{figure}
\centering
\renewcommand{\thefigure}{$\dag$}
\subfloat[Sub-dagger]
{
\label{subfloat:first}
Hello there my good sport
}%
\qquad
\subfloat[Sub-dagger the other]
{
Hello again nice to see you
}
\caption{Daggered figure}
\label{fig:dag}
\end{figure}
Figure \ref{fig:dag} shows two things... one of them is sub-figure \ref{subfloat:first}.
\listoffigures
\end{document}
However, when %\usepackage{hyperref} is uncommented, the following error is given:
! TeX capacity exceeded, sorry [input stack size=5000].
\curr@fontshape ->\f@encoding
/\f@family /\f@series /\f@shape
l.11 \subfloat
[Sub-dagger]
! ==> Fatal error occurred, no output PDF file produced!
No error occurs if no subfloats are in the figure, either. The error occurs even if \listoffigures is commented out.
A remark: if $\dag$ is replaced by $a$, or by ABC, the code compiles fine. It seems like there is some issue with the amount of memory $\dag$ takes, which is strange to me.

