Using a variation of the technique Dissecting paragraphs with \lastbox
described in Section 5.9.6 of TeX by Topic, you can produce a blur effect; the idea is to use two copies for each line and typeset the line and its copies superimposed:
\documentclass{article}
\usepackage{lipsum}
\newbox\flinebox
\newbox\slinebox
\newbox\mlinebox
\def\duplines{\setlength\parindent{0pt}
\setbox\flinebox\lastbox
\ifvoid\flinebox\relax
\else
\setbox\slinebox\hbox{\copy\flinebox}
\setbox\mlinebox\hbox{\copy\flinebox}
\unskip\unpenalty
{\duplines}
\box\flinebox\vspace*{-2.3ex}
\box\mlinebox\vspace*{-2.3ex}
\box\slinebox \fi
}
\newcommand\BlurText[1]{%
\vbox{#1\par\duplines}}
\begin{document}
\BlurText{\lipsum[1]}
\end{document}

In a comment, doncherry suggested horizontally shifting the layers to decrease legibility; this can be done using this definition of \duplines:
\def\duplines{\setlength\parindent{0pt}
\setbox\flinebox\lastbox
\ifvoid\flinebox\relax
\else
\setbox\slinebox\hbox{\copy\flinebox}
\setbox\mlinebox\hbox{\copy\flinebox}
\unskip\unpenalty
{\duplines}
\box\flinebox\vspace*{-2.4ex}
\makebox[\textwidth]{\hspace*{2pt}\box\mlinebox}\vspace*{-2.4ex}
\makebox[\textwidth]{\hspace*{4pt}\box\slinebox}\fi
}
and defining \BlurText as before, here's the new result of \BlurText{\lipsum[1]}:

And a little modification using some color:
\usepackage{xcolor}
and in \duplines:
{\color{black!50}\box\flinebox\vspace*{-2.4ex}
\makebox[\textwidth]{\hspace*{2pt}\box\mlinebox}\vspace*{-2.4ex}
\makebox[\textwidth]{\hspace*{4pt}\box\slinebox}}
