Archive SMS messages, without extra permissions
As you don't ask to restore them (just to backup): Did you take a look at TxtArchive SMS Backup? Yupp, costs a few bucks. But hence it needs no ads, and no internet: Read SMS/MMS, Read Contactdata (both are connected -- you surely want to know who wrote the SMS ;), and store to SD.

Similarly SMS Backup &amp; Restore Pro for about the same price (2 Euro), which also wants to write SMS/MMS (to restore them), and keep the phone from sleeping while it does the work.

Oh, plus the requirement mentioned by Flow: "read phone state and identity" is also required. -- though the app states Android minversion 1.6 (this requirement was removed with Android 2.0 AFAIK -- for all previous versions it was a "must").

Simple search for SMS Backup on the playstore, both on page 1 -- not too hard to find. Hope you like them ;)