Is there an app to save text messages?

I have an iPhone, and there are some texts on it I’d like to save. Is there an app to transfer them to my computer, or better yet, save them on my phone so I can’t accidently delete them when I clear out my junk?

I know there are a number of them for Android, but I have no experience with iPhone applications, but here’s where I’d start.

I know you probably are looking for recommendations from Dopers as well, so consider this a helpful bump as well.

If there aren’t many, you could consider taking screenshots (home + power buttons)

This is the method I use. Then forward them to my computer.

No iDevice apps that I know of. It there are Win and Mac applications that can archive or print text messages. If you are so inclined, you can also do it yourself with a bit of database scripting against the backup file iTunes keeps of your iPhone or iPad.

Just copy & paste them into a note. Make sure you have notes syncing turned on and that will continuously back-up all the notes and their updates to your gmail “all mail” folder (which comes in handy in case the note itself somehow gets deleted or you lose your phone).

There’s a way to do this.
The test messages are stored in an SQL database on the iPhone, and it’s possible to download this database to your Mac and open it with MySQL.
Do a Google search for SMS database iPhone download and you will find the instructions.
ETA: Here, I did it for you: How to Access and Read the iPhone SMS Text Message Backup Files

Reported.