iNoJB - iNoJB, formerly iNoCydia, is an amazing Cydia alternative requiring no jailbreak!
Cydia - An alternative app store for jailbroken devices.
BuildStore - Safe and trustworthy alternative app store for iOS
Apple App Store - Install apps on your iDevice via the App Store.
Altstore - A home for apps that push the boundaries on iOS
Exstensify - iOS tweak store without Jailbreak