How to get store information in Magento?

Question

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