Tim,
autocomplete="off" may not be valid HTML, but it does work.
echo '<form autocomplete="off" id="responseform" method="post" action="', $quiz->thispageurl . '" enctype="multipart/form-data"' .' onkeypress="return check_enter(event);" accept-charset="utf-8">', "\n";
on the other hand, using JavaScript (as per Moodle 1.9) does not work.
echo '<form id="responseform" method="post" action="', $quiz->thispageurl . '" enctype="multipart/form-data"' .' onclick="autocomplete=\'off\'" onkeypress="return check_enter(event);" accept-charset="utf-8">', "\n";
Just tested in moodle 1.9.9 and FireFox.
Joseph