If you're willing to go the latex->dvips->ps2pdf route, Xfig provides an easy solution in conjunction with the [psfrag package]. The discussion below does not have to be produced in Xfig. However, the concepts illustrated was easiest to duplicate using Xfig.
Assume that image.eps was generated in Xfig, looking like this:

Using \psfrag{<tag>}{<LaTeX text>}, you can modify mylabel1 in image.eps to be any LaTeX command, including referencing a theorem (say):
\documentclass{article}
\usepackage{graphicx}% http://ctan.org/pkg/graphicx
\usepackage{psfrag}% http;//ctan.org/pkg/psfrag
\usepackage{hyperref}% http://ctan.org/pkg/hyperref
\newtheorem{theorem}{Theorem}% \begin{theorem}...\end{theorem}
\begin{document}
\begin{figure}[t]
\centering
\psfrag{mylabel1}{Theorem~\ref{thm:first}}%
\includegraphics{image}
\caption{This is a figure}
\end{figure}
\begin{theorem}
This is the first theorem. \label{thm:first}
\end{theorem}
\end{document}

The hyperref package was added to highlight the reference.
As mentioned in the comments. There exists no formal pdffrag counterpart to psfrag. Xfig, however, provides a means around that via xfigfrag. However, development on this stopped on 2009-11-28. See the xfigfrag README on how to use this tool.
For the moment, an experimental pdffrag exists in the form of the pdfrack package. Although I haven't used it in a setting that requires referencing (or any setting for that matter).
xfigcan be configured to let LaTeX render all text inside an xfig figure (and probably is one of the reasons so many people still use this rather archaic program). With OmniGraffle, I only see a possibility if you export your figures to EPS and switch over to the dvi->ps->pdf route to be able to usepgsfrag. – Daniel Jul 01 '11 at 07:25overpicI also recommend the TikZ based solution shown in Drawing on an image with TikZ, which will be part of the TeX.SX bundle. – Martin Scharrer Jul 01 '11 at 11:36