There is an easy way actually. So easy that I'm surprised I've never seen it mentioned. But it only works under the following conditions: the left column must be floated left and the right column must not be floated but use a left margin (or vice versa).
I made the borders thick and in different colors so you can see how I mean more easily. If you give the right column a left margin that is as wide as the left column and any padding and left border it may have, but does NOT include the width of its right border, the right column's left border will be covered by the left column's right border, so no matter which column is longest there will always be a single-width border showing all the way down.
HTML
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN"
"http://www.w3.org/TR/html4/strict.dtd">
<head>
<title>Shared column border</title>
<style type="text/css">
<!--
#left { width: 500px; float: left;
border-right: 8px solid #444 }
#right { margin-left: 500px;
border-left: 8px solid red }
-->
</style>
<div id="left">
<p>
When you modify a document, its little disk icon in the tab turns red. This visual cue makes it easy to identify documents that need saving if you want to preserve the changes. When you save the document, its disk icon becomes gray again. </p>
<p>
You will find many useful commands in the Modify menu that help you process your text. These commands make it easy to join or split lines, sort lines, indent or unindent lines, change alignment and character case, insert bullets or line numbers, strip HTML tags or convert text to HTML, etc.</p>
</div>
<div id="right">
<p>
When you modify a document, its little disk icon in the tab turns red. This visual cue makes it easy to identify documents that need saving if you want to preserve the changes. When you save the document, its disk icon becomes gray again. </p>
<p>
You will find many useful commands in the Modify menu that help you process your text. These commands make it easy to join or split lines, sort lines, indent or unindent lines, change alignment and character case, insert bullets or line numbers, strip HTML tags or convert text to HTML, etc.</p>
<p>
When you modify a document, its little disk icon in the tab turns red. This visual cue makes it easy to identify documents that need saving if you want to preserve the changes. When you save the document, its disk icon becomes gray again. </p>
<p>
You will find many useful commands in the Modify menu that help you process your text. These commands make it easy to join or split lines, sort lines, indent or unindent lines, change alignment and character case, insert bullets or line numbers, strip HTML tags or convert text to HTML, etc.</p>
<p>
When you modify a document, its little disk icon in the tab turns red. This visual cue makes it easy to identify documents that need saving if you want to preserve the changes. When you save the document, its disk icon becomes gray again. </p>
<p>
You will find many useful commands in the Modify menu that help you process your text. These commands make it easy to join or split lines, sort lines, indent or unindent lines, change alignment and character case, insert bullets or line numbers, strip HTML tags or convert text to HTML, etc.</p>
</div>
</body>
</html>