You have a couple of issues with your output. First, it's not clear from your example if you have the actual select element parent, and I'm not sure if browsers will display options without a parent select. Second, you are not escaping your array variables. So this might fix it:
$sql = "SELECT user_id, user_name FROM users"; $result=mysql_query($sql);
echo '<select name="users">';
while($row = mysql_fetch_array($result)) {
echo '<option value="'. $row['user_id'] . '">' . $row['user_name'] . "</option>\n";
}
echo '</select>';