iOS (Jailbreak): If you don't want Safari saving your browsing history, you have to make your way into the Settings menu and enable Private Browsing. This can be a bit cumbersome when you're just looking for a quick switch. Privata is a jailbreak tweak that adds a private browsing toggle right in Safari.
Once Privata is installed, you simply tap the action button at the bottom of Safari (in the middle), and then tap "Toggle Private Browsing". When you're in private browsing mode, the screen changes to a darker colour, and it won't save or record your browsing. Alternative browsers have this built in too, but Privata is ideal for Safari fans who just want a quick toggle for privacy. Privata is a free download in the ModMyi repository.