iNoJB - iNoJB, formerly iNoCydia, is an amazing Cydia alternative requiring no jailbreak!
Cydia - An alternative app store for jailbroken devices.
Apple App Store - Install apps on your iDevice via the App Store.
BuildStore - Safe and trustworthy alternative app store for iOS
Sileo - An APT package manager for jailbroken iDevices.
OpenAppMkt.mobi - OpenAppMkt.mobi is an app store for HTML5 mobile apps.