Lots of iPhone users have the same trouble. that is they can't backup the SMS to anywhere when the SMS box is full, then they have to delete all of them to prevent iPhone rejecting new SMS receiving. so here i introduce a useful tool, hope that it can help you

Tansee iPhone Transfer SMS
With Tansee iPhone Transfer SMS, you can transfer the iPhone SMS to computer as a txt file or a ANTS file before the event above happens. Before the transfer, you can choose to transfer from all contacts or a single contact, further more, you can choose transfer the SMS to a TXT file or a ANTS file. In ANTS file condition, you can protect the file with a password to keep your privacy. From now on ANTS file support edit feature just the same operation process as the SMS edit on iPhone. If you want print iPhone SMS, you can choose MHT file format, then open the file by Internet Explorer, print it just like shown on iPhone!

Tansee iPhone Transfer SMS can provide you:
* Backup SMS in iPhone to computer before iPhone reject receiving new SMS.
* View and Manage old iPhone SMS in your computer.
* View SMS in Text file format (.txt file), ANTS file format (.ants file), MHT file format (.mht file)on PC.
* Password protection support (ANTS file only).
* Edit SMS (ANTS file only)
* Print SMS (MHT file print by IE).

for more information: http://www.applesw.com/iphone-software/other/Tansee-iPhone-Transfer-SMS.html
derect download link: http://www.regnow.com/softsell/visitor.cgi?affiliate=508560&action=site&vendor=13181&ref=http://www.applesw.com/download/Tansee-iPhone-Transfer-SMS.zip

Other software:

backup iphone songs/videos/contacts/SMS/books to computer
Cucusoft iPhone Tool Kits is an easy to use utility designed to help you back up all your files on your iPhone, so that you can recover any lost or missing songs, videos, books, photos and so on.

Cucusoft iPhone Tool Kits can easily backup and transfer iPhone songs, videos, photos, SMS, call list, contacts and books(you purchased via iBook Store) to computer. And even enable your iPhone as a removable hard disk.

"iPhone Tools Kits" Transfer is a must-have utility to keep your iPhone safe if you have an iPhone. It supports iPad, iPod touch as well.

for more information: http://www.applesw.com/iphone-software/other/Cucusoft-iPhone-Tool-Kits.html