Mage::app()->getStore()->getFrontendName();

Mage::app()->getStore()->getStoreId();

Mage::app()->getStore()->getCode();

This returns store code, e.g. 'en' for a storefront that is setup for English and called 'en', and not the numerical id.

Mage::app()->getStore()->getIsActive();

Mage::app()->getStore()->getWebsiteId();

Mage::app()->getStore();

Returns an instance of Mage_Core_Model_Store

Mage::app()->getStore()->getGroup()->getName()

Mage::app()->getStores();

Returns an array of Mage_Core_Model_Store models.