While there are ready made apps that backup and restore your SMSes, you can easily backup the database if you have a rooted phone without installing any external software.
The SMSes are stored in an SQLite database available under:
/dbdata/data/com.android.providers.telephony/databases/mmssms.db
Here is the procedure:
$ sudo ./adb start-server $ ./adb pull /dbdata/data/com.android.providers.telephony/databases/mmssms.db ~/sms_backup.db
Simple!