Here is the link to direct download (no ad, no spyware)
MySmsBackup can be used to export all SMS messages on an Android phone to a text file on the memory of the phone.
MySmsBackup can also be used to synchronize all SMS messages on an Android phone to a Gmail account. In order to do that, you just have to create a Gmail account on your phone and then install MySmsBackup and select the account that will be detected automatically by the application. Then you enter your password and the first synchronization begins.
Then, in any further synchronization only new SMSes will be sent to the Gmail account.
The application is still in beta release, but will make you able to backup your SMS for further use (for printing them for example).
Very soon it will integrate the backup of MMSes and also the ability to export and import to and from an XML file.