Magento get current url of a page

Magento core url helper allows you to get current url.

To get current url in magento you just need one line of code as below:

ref: public function getCurrentUrl()

$magentoCurrentUrl = Mage::helper('core/url')->getCurrentUrl();

You can also get current url as base64 encoded url as:

$magentoCurrentUrlBase64 = Mage::helper('core/url')->getCurrentBase64Url();
or,
$magentoCurrentUrlBase64 = Mage::helper('core/url')->getEncodedUrl($url);
// $url is optional

Same helper allows you to get home url which is base url:

$magentoHomeUrl = Mage::helper('core/url')->getHomeUrl();

Source: app\code\core\Mage\Core\Helper\Url.php

Functions used above as they appear on magento core url helper are as below:

    /**
     * Retrieve current url
     *
     * @return string
     */
    public function getCurrentUrl()
    {
        $request = Mage::app()->getRequest();
        $port = $request->getServer('SERVER_PORT');
        if ($port) {
            $defaultPorts = array(
                Mage_Core_Controller_Request_Http::DEFAULT_HTTP_PORT,
                Mage_Core_Controller_Request_Http::DEFAULT_HTTPS_PORT
            );
            $port = (in_array($port, $defaultPorts)) ? '' : ':' . $port;
        }
        $url = $request->getScheme() . '://' . $request->getHttpHost() . $port . $request->getServer('REQUEST_URI');
        return $url;
    }

    /**
     * Retrieve current url in base64 encoding
     *
     * @return string
     */
    public function getCurrentBase64Url()
    {
        return $this->urlEncode($this->getCurrentUrl());
    }

    public function getEncodedUrl($url=null)
    {
        if (!$url) {
            $url = $this->getCurrentUrl();
        }
        return $this->urlEncode($url);
    }

    /**
     * Retrieve homepage url
     *
     * @return string
     */
    public function getHomeUrl()
    {
        return Mage::getBaseUrl();
    }