First of all, what you are doing looks like a table to me, so you might want to consider that. Doing it with CSS however is a bit more tricky (unless you do the table styling in CSS). The following code works but does not center vertically the text in the box:
<html><head><title>Test2</title></head><body>
<div style="width:300px; padding: 2px; border: 1px solid black;">
<div style="float:right; width: 100px;">
<div style="border: 1px solid black; margin-bottom: 2px;">
Here is some sample text. And some additional sample text.
</div>
<div style="border: 1px solid black;">
Here is some sample text. And some additional sample text.
</div>
</div>
<div style="border: 1px solid black; margin-right: 102px;">
<div>
This column should equal the height (no fixed-height allowed) of the 2 rows sitting to the right.
</div>
<div style="clear: right; margin-bottom: -1px;"></div>
</div>
</div></body></html>
Table cells in CSS are easier:
<!DOCTYPE html>
<html><head><title>Test2</title></head><body>
<div style="display: table; width:300px; border: 1px solid black; border-spacing: 2px;">
<div style="display: table-cell; border: 1px solid black; vertical-align: middle;">
This column should equal the height (no fixed-height allowed) of the 2 rows sitting to the right.
</div>
<div style="display: table-cell; width: 100px;">
<div style="border: 1px solid black; margin-bottom: 2px;">
Here is some sample text. And some additional sample text.
</div>
<div style="border: 1px solid black;">
Here is some sample text. And some additional sample text.
</div>
</div>
</div>
</body>
</html>