I was trying to figure out if there was a way to save messages in iOS’s Messages (I discovered that my iCloud backup has them, but cannot read them separately). I found two apps that could do so, PhoneView and Touch Copy. But one is $25, and the other is $30!
I must be out of touch with the pricing of apps these days! Is there something uniquely difficult about this feature that commands that kind of price, or is it just the standard “expected” layout for such things?
How about this?
Open text message.
Place finger on text message for several seconds until magnifying glass appears
Select all
Hit copy
Open Notes
Place finger on note until magnifying glass appears
Select paste
Close notes
You may now send me $30. 
Here’s my guess: This is a niche product. Most people don’t want to save all their text messages, so there are few buyers. One group that might want to save them all are people involved in legal battles where the contents are evidence, and they’re willing to pay high prices. People who want to just save a few here and there use Rick’s method.
Androids have numerous free apps to back up and restore all texts, including an app that uses a folder in your gmail account as a repository. Aren’t there any other options in the i-world?
If you just want to save a record of certain messages:
If you’re on a Mac, and you’ve synced a backup, this will get more detail than you could possibly want:
find ~/Library/Application\ Support/MobileSync/Backup/ -name 3d0d7e5fb2ce288813306e4d4636395e047a3d28 -exec sqlite3 {} .dump \;
(all on one line in Terminal)
I think if you jailbreak you can do it for free? Does anyone know?
The two methods I posted above work without jailbreaking. Someone with more knowledge of sqlite3 than I, and time to dig into the schema, could construct a SELECT query for the second to just display the main fields.
I’ve recommend this in the past, and it works perfectly.