If you are using MAC, and want to backup your iPhone sms onto your mac, here is another tip.
this iPhone SMS to Computer Transfer for Mac can help you transfer iPhone SMS to Mac to avoid missing of the valuable messages. And it can also help you copy Music, Video, Podcast, TV Show files from iPhone to Mac.

http://gutensoft.com/Utilities/transfer-iphone-sms-to-mac.html

What's more, this iPhone SMS to Computer Transfer for Mac can sync iPhone library to iTunes directly and even fully supports the latest iOS 4.3, iOS 5 beta, iTunes 10.3 and iTunes 10.5 beta. Besides, you can even browse your iPhone, iPad or iPod touch as a portable hard disk after connect the iPhone to Mac.

It supports all types of iPhone/iPod/iPads including iPad, iPad 2, iPhone 3G, iPhone 3GS, iPhone 4, iphone 4s, iPod classic, iPod shuffle, iPod shuffle 6G, iPod nano, iPod nano 5G, iPod nano 6G, iPod touch, iPod touch 4, etc.

If you're looking to transfer iPhone SMS between iPhone and computer, Backuptrans iPhone SMS Backup & Restore is the best choice which lets you do it in just a few easy steps. It offers all solutions for all serious iPhone users. It not only supports iPhone SMS to computer backup & export, but also enables users to restore SMS backup from computer database to a new iPhone or back to your old iPhone. No other iPhone utility softtware does more. It supports both Windows and Mac.

Features:
1 Backup iPhone SMS to computer
2 Restore SMS to iPhone from PC
3 Export iPhone SMS to document files such as txt, csv, doc or html
4 Import SMS to iPhone from iTunes Backup
5 Print out iPhone SMS messages in conversations
6 iMessage supported also

Read more: http://www.backuptrans.com/iphone-sms-backup-restore.html

If you want to transfer old iPhone Contact to your new iPhone, how to do it in easy way? You can use this soft to manage your iPhone contacts without iTunes. It can do:
• Transfer songs, videos, playlists, iTunes U, Podcasts to & from Your PC/iTunes
• Copy photos & albums to/from Your PC & iDevice
• Fully Manage Your iPhone Contacts & SMS without iTunes
• Automatically convert to iDevice-compatible music & video formats during transfer.
• Transfer files directly between iPhone, iPod and iPad with a click.
• 100% compatible with iPhone 5, 4S, iPod touch 4, 5, iPad mini, the new iPad, & more!

Read more:
How to Transfer Files Between iPhone and Computer
http://www.transfer-iphone-recovery.com/transfer-files-between-iphone-and-computer.html
How to Transfer from iPhone to iPhone
http://www.transfer-iphone-recovery.com/transfer-contact-from-iphone-to-iphone.html

If the restore process won't work, because you have a different iOS version or your backup is corrupt or simply it doesn't want to restore I would recommend to try open your backup using iPhone Backup Extractor, Mac, Windows and Linux version. I found an interesting article on their site on how to recover data from a corrupt backup, thought worth sharing this bit of info: http://www.iphonebackupextractor.com/blog/2012/jul/25/retrieve-data-from-corrupt-iTunes-backup/

iPhone Message Transfer Tool is what I would recommend for this.

jonespat's link not work at all.
If you want to backup iPhone SMS to computer or print out iPhone sms, simply go to the easy iPhone sms to computer direct transfer tip
http://www.gutensoft.com/Utilities/Tansee-iPhone-Transfer-SMS.htm

@Nasam

Please check it again, link is working perfectly.

You can use this powerful all-in-one Phone to Phone Data Transfer

Wondershare MobileTrans is a powerful phone to phone data transfer tool lets you seamlessly copy data between Android, Symbian and iOS phones.,no matter Android phone (HTC, Samsung, etc.), Symbian phone (Nokia, Motorola, etc.) or iOS phone (iPhone 5, iPhone 4S, etc).You can selectively transfer data between any two of them without data loss.Moreover, Directly transfer from one phone to another

For Android:

http://www.recovery-iphone.com/phone-to-phone-data-transfer.html

For iOS iphone/ipod/ipad:

http://www.recovery-iphone.com/iphone-ipad-ipod-manager.html

No need to follow such lengthy procedure just look at this step-by-step guide which shows how to backup iPhone SMS to computer:

http://www.iphone-to-pc.com/how-transfer-messages-iphone-pc.html

Recover iphone all lost data,Recover iPhone Contacts, Messages,Photos,Videos, Camera Roll, Photo Stream, Photo Library, Message Attachments, Call History, Calendar, Notes, Voice Memos, Reminders and Safari Bookmarks

For iPhone recovery on Mac:
http://z0download.com/detail/iPhone-iTunes-Data-Recovery-Mac

For iPhone recovery on Windows computer:

http://z0download.com/detail/iPhone-5-iTunes-Data-Recovery

Backup all iphone sms contact,music to computer

http://z0download.com/detail/Cucusoft-iPhone-Backup-Tool-Kits

jonespat's link not work at all.
If you want to backup iPhone SMS to computer or print out iPhone sms, simply go to the easy iPhone sms to computer direct transfer tip
http://www.manage-iphone.com/a/win

Get Back Your Lost Contacts, Photos, Messages and More.
Freaking out cause you accidently deleted photos, text messages or other crucial stuff on your iPhone, iPad or iPod Broke or damaged your iPhone or iPod and now the data’s gone? Failed updates kill your data? The bottom line is, whatever the problem, the doctor is in! Wondershare Dr.Fone is an easy-to-use tool that can help you easily recover photos & videos, contacts, SMS, call logs, memos and calendars, even Safari bookmarks you thought you’d lost forever!
Now you can try from here. http://www.manage-iphone.com/
In addition,free download: http://hotdownloads.com/trialware/download/Download_drfone_full1283.exe?item=8799-322&affiliate=605715

If you were to restore from a backup then your text messages will be back on your device.
I believe you can also find the text message file and drag it into iTunes that should work also.
If you've backed up your iPhone to iCloud and it gets wiped or replaced, restoring from that backup will restore your iPhone SMS messages up to computer in the time you last backed up to iCloud.
• Backup SMS from iPhone to Computer

http://www.video-converter-mac.org/iphone-sms-to-mac-transfer/
• Restore Text Message from iTunes backup

http://www.video-converter-mac.org/iphone-sms-recovery/

Hopefully it works for you guys.

You can use this software I have ever tried for recovering messages for iPhone.This program can help you recover deleted or formatted photos, video, audio files, documents and archives stored in the SD card inside your iphone. It supports with all iphone models and guarantees 100% security.Here is the details for you, take a look if you need, hope I can help you.
http://www.manage-iphone.com/
Free try:
for mac:http://download-affiliate.wondershare.com/605715/WondershareDr.Fone.dmg

for PC: ( iphone5)
http://hotdownloads2.com/trialware/download/Download_drfone_full1283_iphone5_.exe?item=8799-323&affiliate=605715

(iphone4s):
http://hotdownloads2.com/trialware/download/Download_drfone_full1283.exe?item=8799-322&affiliate=605715
(iphone4):
http://hotdownloads2.com/trialware/download/Download_Wondershare_Dr.Fone_iPhone_4.exe?item=8799-313&affiliate=605715
In addition: Youtube has more tips:
http://www.youtube.com/watch?v=PkV13hzDmww&feature=youtu.be

If you want to backup and tranfer you iphone data to PC or Mac.more useful guide from here:

For Mac: http://www.manage-iphone.com/a/mac

For PC: http://www.manage-iphone.com/a/win

goodluck

How to Transfer Music from iPhone to PC: http://www.leawo.com/knowledge/iphone-4-music-transfer.html

How to Transfer Videos from iPhone to Computer:
http://www.leawo.com/knowledge/iphone-4s-to-computer-transfer.html

For messages transferring from old iphone to iphone 4s, try MobileTrans. Works fine for my iPhone 4S. Contacts transferring is also supported.
http://software.bigbigsoft.com/phone-transfer

Well, you can read this:
http://www.istonsoft.com/iphone/transfer-contacts-from-iphone-to-ipad.html
The operation is similar.