Adding vertical lines to each side of a paragraph

You can use the mdframed package; a little example:

\documentclass{article}
\usepackage{mdframed}
\usepackage{lipsum}% just to generate text for the example

\newmdenv[
  topline=false,
  bottomline=false,
  skipabove=\topsep,
  skipbelow=\topsep
]{siderules}

\begin{document}

\lipsum[4]
\begin{siderules}
\lipsum[1-5]
\end{siderules}
\lipsum[4]

\end{document}

Here's a simplemodification placing the rules in the margin (now the text width inside the environment is equal to the default \textwidth):

\documentclass{article}
\usepackage{mdframed}
\usepackage{lipsum}% just to generate text for the example

\newmdenv[
  topline=false,
  bottomline=false,
  skipabove=\topsep,
  skipbelow=\topsep,
  leftmargin=-10pt,
  rightmargin=-10pt,
  innertopmargin=0pt,
  innerbottommargin=0pt
]{siderules}

\begin{document}

\lipsum[4]
\begin{siderules}
\lipsum[1-5]
\end{siderules}
\lipsum[4]

\end{document}

With results similar to Gonzalo's answer but made with tcolorbox.

\documentclass{article}
\usepackage{lipsum}% just to generate text for the example

\usepackage[most]{tcolorbox}

\newtcolorbox{tcbsiderules}[1][]{blanker, breakable, 
     left=3mm, right=3mm, top=1mm, bottom=1mm,
     borderline vertical={1pt}{0pt}{black},
     before upper=\indent, parbox=false, #1}


\begin{document}

\lipsum[1]
\begin{tcbsiderules}[oversize]
\lipsum[2-4]
\end{tcbsiderules}
\begin{tcbsiderules}
\lipsum[5-7]
\end{tcbsiderules}
\lipsum[8]

\end{document}