If you just want to back up your SMS messages, all you need to do is do a normal sync to your PC as that backs up your SMS messages as well. The folder location varies by OS release, but you can find yours on the Apple support page (support.apple.com/kb/ht4946). The SMS database is a file named "3d0d7e5fb2ce288813306e4d4636395e047a3d28" and it's stored in SQLite format, so you can view it with a SQLite viewer. The problem is it's not stored in a way that you could meaningfully read conversations, so that's where 3rd party programs are useful.
Originally Posted by jonesyvoor
I wasn't happy with the existing 3rd party apps, so I actually created one of my own. It's called AllYourTexts. It allows you to view your texts in normal conversation form and allows you to export them as plaintext or HTML. There are also a few little bells and whistles like showing you statistics and graph visualizations of your texting behavior. It's $9.99 but there's a 15-day free trial where you can use all the features of the program (a lot of the other programs only allow you to view a few of your messages in the trial).
I can't link because this is my first post, but you can try out the program at allyourtexts.com.