You can forward them to your e-mail. Google Play has apps for Android phones that will backup texts and e-mail them to you automatically; wonder if the WP store has something similar?
Hi hgoolsbyrn! I hope you're enjoying your awesome phone. Skydrive, as drichter mentioned, is a great way to be able to back up your text messages and more. Please visit http://windows.microsoft.com/en-US/skydrive/download for all the information about this great service from Microsoft for your WP8 device.
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