jDownloads is free and popular Joomla extension for downloads manager.
This tutorial works for jDownloads 1.9.0 version for Joomla 2.5
To remove copyright footer message, open the folder components/com_jdownloads and edit the file jdownloads.php
Find (use ctrl+F) and remove the following lines of code:
$footer .= '<div style="text-align:center" class="jd_footer"><a href="http://www.jDownloads.com" target="_blank" title="www.jDownloads.com">'.$power.'</a></div>';