Your iPhone stores thousands of text messages. This seems like a lot until you realize how quickly a few threads fill up with hundreds of messages each. If you're on Mac, there's a nice little freeware utility called SyPhone that archives your SMS messages for you. Once you start it up, it will back up your iPhone's SMS messages through a helper app, so you don't even need to think about it. When you open SyPhone you can view all these messages in threads like on your iPhone.
SyPhone works by copying the messages from the backup of iPhone that iTunes makes each time you sync, so make sure you've recently connected before deleting new messages you want to save.
Archive Text Messages
