Currently Being ModeratedDec 28, 2012 10:19 AM (in response to lunaman63)
Text messages are included in the iPhone backup on your computer or in iCloud. If you back up to your computer there are 3rd party apps that can extract data from your iPhone backups. Do a search using your favorite search engine for "iPhone backup extractor".
Currently Being ModeratedJan 3, 2013 6:32 AM (in response to lunaman63)
You can also try to export your iPhone SMS messagess to your PC using third-party tools.
If your main aim is to backup your iPhone text messages (without necessarily having them displayed on your PC), I would advise you to turn iCloud backup on by going to Settings > iCloud > Storage & Backup and turn "iCloud Backup" to ON. The iCloud backup will back up your iPhone text messages, contacts, and other data so that you can restore it back should you need to in the future.