Depending on your site design, you might want to make the login block less prominant. Rather than hiding it all together, why not use the Forms API to turn it into a collapsible form?

Here's an example of how to do that with a mini module:

//for Drupal 4.7
/**
 * Implementation of hook_help().
 */
function loginmod_help($section) {
  switch ($section) {
    case 'admin/modules#description':
      return t('Makes login block collapsible');
  }
}

/**
 * Implementation of hook_form_alter().
 */
function loginmod_form_alter($form_id, &$form) {

  if ($form_id == 'user_login_block'){
          $form['lmod'] = array('#type' => 'fieldset', 
                                '#title' => 'Member login', 
                                '#collapsible' => TRUE, 
                                '#collapsed' => TRUE);
          $form['lmod']['name'] = $form['name'];
          $form['lmod']['pass'] = $form['pass'];
          $form['lmod']['submit'] = $form['submit'];
          $form['lmod']['links'] = $form['links'];
          unset($form['name']);
          unset($form['pass']);
          unset($form['submit']);
          unset($form['links']);
  }
}

Be sure to remove the last ?> and save as a text file in your modules directory as loginmod.module.

You may also want to include some styling in your theme's style.css to get rid of the block title and borders (note that the exact tags will depend on your theme):

#sidebar-right #block-user-0 {border: 0px; }
#sidebar-right #block-user-0 h2{	border: 0px;	display: none;}
#sidebar-right #block-user-0 .content{ margin-top: 1em; }

As an alternative, here's code for an entriely new block defined by the module. Use this instead of loginmod_form_alter. Enable this block instead of the core login block. Note that this gives you a "logout" link in place of the login form once the user is authenticated.

function loginmod_block($op = 'list', $delta = 0, $edit = array()) {
  global $user;

  if ($op == 'list') {
     $blocks[0]['info'] = t('Collapsible User login/logout');
     return $blocks;
  }
  elseif ($op == 'view') {
    $block = array();

    switch ($delta) {
      case 0:
        if (!$user->uid) { //user is not authenticated
          $form['#action'] = url($_GET['q'], drupal_get_destination());
          $form['#id'] = 'user-login-form';
	  $form['lmod'] = array(
            '#type' => 'fieldset', 
            '#title' => '<b>Member login</b>', 
            '#collapsible' => TRUE, 
            '#collapsed' => TRUE);
          $form['lmod']['name'] = array('#type' => 'textfield',
            '#title' => t('Username'),
            '#maxlength' => 60,
            '#size' => 15,
            '#required' => TRUE,
          );
          $form['lmod']['pass'] = array('#type' => 'password',
            '#title' => t('Password'),
            '#size' => 15,
            '#required' => TRUE,
          );
          $form['lmod']['submit'] = array('#type' => 'submit',
            '#value' => t('Log in'),
          );

          if (variable_get('user_register', 1)) {
            $items[] = l(t('Create new account'), 'user/register', array('title' => t('Create a new user account.')));
          }
          $items[] = l(t('Request new password'), 'user/password', array('title' => t('Request new password via e-mail.')));
          $form['lmod']['links'] = array(
             '#value' => theme('item_list', $items));

          $block['subject'] = '';
          $block['content'] = drupal_get_form('lmod_user_login_block', $form, 'user_login');
        }
	else {  //user is authenticated, show logout link
          $block['subject'] = '';
          $block['content'] = '<div id="logout"><b>'.l(t('Log out'),'logout', array('title' => 'Log out of the website')).'</b></div>';		
	}
        return $block;
    }
  }
}