How to add simple account / logout links where login changes to logout when signed in ( login / register ) for cms magento 1.x ?

Just insert this code into your phtml:

   <div class="account-links">
        <?php
        if ($this->helper('customer')->isLoggedIn()) {
            ?>
            <a href="<?php echo Mage::getUrl('customer/account'); ?>">Account</a>
            <a href="<?php echo Mage::getUrl('customer/account/logout'); ?>"><?php echo $this->__('Log out'); ?></a>
        <?php } else {
            ?>
            <a href="<?php echo Mage::getUrl('customer/account/login'); ?>"><?php echo $this->__('Log in'); ?></a>
            <span> or</span>
            <a href="<?php echo Mage::getUrl('customer/account/create'); ?>"><?php echo $this->__('Register'); ?></a>
        <?php } ?>
   </div>

OR

        <?php
        if ($this->helper('customer')->isLoggedIn()) {
            ?>
            <span class="widget widget-cms-link-inline"><a href="<?php echo Mage::getUrl('customer/account'); ?>">Account</a></span>
            <span class="widget widget-cms-link-inline"><a href="<?php echo Mage::getUrl('customer/account/logout'); ?>"><?php echo $this->__('Log out'); ?></a></span>
        <?php } else {
            ?>

            
            <span class="widget widget-cms-link-inline"><a href="<?php echo Mage::getUrl('customer/account/create'); ?>"><?php echo $this->__('Register'); ?></a></span>
            <span class="widget widget-cms-link-inline"><a href="<?php echo Mage::getUrl('customer/account/login'); ?>"><?php echo $this->__('Log in'); ?></a></span>            
        <?php } ?>

ALSO YOU CAN USE

<?php 
    if( ! Mage::getSingleton('customer/session')->isLoggedIn()){
        //not logged in
    }else{
        // logged in
    }
?>