If, for example, you only want to draw the top and bottom border of a box, or perhaps the left and bottom only, is there a simple package to do this or must one resort to using tables or heavy-weight drawing tools like tikz?
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The mdframed package has what you want. Here is a MWE that demonstrates the borders you described in three new environments.
There are many other options available- see the documentation for more details and examples.

\documentclass{article}
\usepackage{mdframed}
\usepackage{lipsum}
% all 4 borders
\newmdenv{allfour}
% just top and bottom
\newmdenv[leftline=false,rightline=false]{topbot}
% just left and bottom
\newmdenv[topline=false,rightline=false]{leftbot}
\begin{document}
\subsection*{all four borders}
\begin{allfour}
\lipsum[1]
\end{allfour}
\subsection*{top and bottom}
\begin{topbot}
\lipsum[2]
\end{topbot}
\subsection*{left and bottom}
\begin{leftbot}
\lipsum[3]
\end{leftbot}
\end{document}
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