Get store data
Mage::app()->getStore();
Store Id
Mage::app()->getStore()->getStoreId();
Store code
Mage::app()->getStore()->getCode();
Website Id
Mage::app()->getStore()->getWebsiteId();
Store Name
Mage::app()->getStore()->getName();
Store Frontend Name (see @Ben's answer)
Mage::app()->getStore()->getFrontendName();
Is Active
Mage::app()->getStore()->getIsActive();
Homepage URL of Store
Mage::app()->getStore()->getHomeUrl();
Current page URL of Store
Mage::app()->getStore()->getCurrentUrl();
All of these functions can be found in class Mage_Core_Model_Store
File: app/code/core/Mage/Core/Model/Store.php
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