iOS (jailbreak): iOS 7 does not give you a way to delete all your text messages at once. If you would like to add that functionality, all you need is a jailbroken device and this free tweak from Cydia.
While you can delete multiple messages within a conversation thread (tap and hold a message bubble, then click more; you'll see it), there's no way to delete more than one conversation thread at once. You have to slide each thread and then tap delete. Head to the Cydia Store and install the free DeleteAllMessages tweak, and you'll then be able to delete everything at once.