In addition to the main change in the loop, there are some other changes I made for better syntax... Make note of them and apply them accordingly when you code.
<?php //Note the addition of the php after the <?. Always use long tag syntax.
$query = mysql_query("select * from players") or die(mysql_error());
while($row = mysql_fetch_array($query)) {
print '<option />' . $row['name']; // Note the removal of the </option> tag and the addition of the / in the <option /> tag. It better follows the HTML/XML guidelines established by the W3C.
}
?>