While contacts, and other important information easily gets synced to your Gmail account, but SMS is one thing – you will need to backup everytime you are changing phones/factory reset or even applying new custom ROM.
There are a few handy applications available in the Android market, which will easily help you make the back up of your text messages.
Backup to Gmail:
1. SMS Backup: It automatically backs up SMS messages to your Gmail account.
2. SMS Backup+: Yes, that + is there for a reason. This app automatically backup SMS, MMS and call log entries using a separate label in Gmail / Google Calendar. It is also possible to restore SMS and call log entries back to the phone (MMS not supported yet).
Backup on SD card:
1. SMS Backup & Restore: A simple app to backup SMS on the SD Card, which can be restored later.
2. SMS Backup & Restore: Offer similar functionality as the above app, this application takes backup of your SMS into file which is stored on your SD card (location : /sdcard/SMSBackup/) and same will be used to restore on the same or other device.