How to replace all pictures by white rectangles?

Well then, just patch graphicx to not output the text:

\documentclass{article}

\usepackage[draft]{graphicx}
\usepackage{etoolbox}

\makeatletter
\patchcmd{\Gin@setfile}{\rlap}{\@gobble}{}{%
  \GenericWarning{}{Failed to patch \protect\Gin@setfile}}
\makeatother

\begin{document}

\noindent\includegraphics[width=\textwidth]{tiger}

\end{document}

This code makes use of the etoolbox package.

My attempt was to redefine \includegraphics:

\documentclass{article}
\usepackage{lipsum}% http://ctan.org/pkg/lipsum
\usepackage{letltxmacro}% http://ctan.org/pkg/letltxmacro
\usepackage{xparse}% http://ctan.org/pkg/xparse
\usepackage{graphicx}% http://ctan.org/pkg/graphicx

\LetLtxMacro{\oldincludegraphics}{\includegraphics}
\RenewDocumentCommand{\includegraphics}{O{} m}{% \includegraphics[..]{...}
  \begingroup\setlength{\fboxsep}{-\fboxrule}%
  \fbox{\phantom{\oldincludegraphics[#1]{#2}}}\endgroup%
}

\begin{document}

\lipsum[1-2]
\begin{figure}
  \centering
  \oldincludegraphics[height=3cm]{tiger} \quad 
  \includegraphics[height=3cm]{tiger} \quad
  \fbox{\phantom{\oldincludegraphics[height=3cm]{tiger}}}
  \caption{This is a tiger}
\end{figure}
\lipsum[3-5]

\end{document}

In the above example, the three images use (i) the original \oldincludegraphics command, followed by (ii) the newly redefined \includegraphics command, followed by (iii) an \fbox{\phantom{\oldincludegraphics{...}}} without the proper \fboxsep set, merely as an illustration of what modification does. The grouping (via \begingroup and \endgroup) within \includegraphics makes sure that setting \fboxsep=-\fboxrule is only local.

letltxmacro provides an effective means to store (or copy) commands that have optional arguments (in this case, the original \includegraphics from the graphicx package), while xparse provides an easy means for specifying commands with (possibly intermixed) optional parameters through \RenewDocumentCommand.

For a quick hack, you can edit graphics.sty (in my case, it is /usr/share/texmf-texlive/tex/latex/graphics/graphics.sty) and find where is filename written inside the rectangle (here, it is line 223, containing \rlap{ \ttfamily\expandafter\strip@prefix\meaning\@tempa}%). Comment it out, that's it.