Create a custom template file (e.g. block--user--login.tpl.php). Then you can add custom classes to the
<div id="user-login-block-container">
<form action="<?php print $form['#action']; ?>" method="post" id="<?php print $form['#id']; ?>"
accept-charset="UTF-8">
<div class="form-item form-type-textfield form-item-name customclass">
<?php print render($form['name']); // Name field ?>
</div>
<div class="form-item form-type-password form-item-pass customclass">
<?php print render($form['pass']); // Password field ?>
</div>
<input type="hidden" name="form_id" value="user_login_block"/>
<div class="form-item form-actions form-wrapper" id="login_button">
<input value="Login" type="submit" class="submit-button customclass" title="Login"/>
</div>
</form>
</div>
Then put in the template.php of your theme, the function:
yourtheme_preprocess_page(&$vars, $hook) {
$user_login = user_login_block(array());
$form = drupal_build_form('user_login_block', $user_login);
$form['name']['#required'] = false;
$form['pass']['#required'] = false;
$vars['form'] = $form;
Finally include the template file in your page.tpl.php:
<?php include 'block--user--login.tpl.php'; ?>