WRONG RWY LNDG AT SEA; WA.

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SEA APCH CLRED ME FOR THE ARR; RWY 16R (A VFR ARR PROC). APPROX 10-12 MI NW OF ARPT; I SWITCHED TO SEA TWR (VERY QUIET FREQ AT THE TIME) AND THE CTLR CLRED ME DIRECT TO THE NUMBERS AND CLRED ME TO LAND ON RWY 16R TO FOLLOW A BRASILIA ON A 4 MI FINAL. AS I APCHED THE ARPT (APPROX 2-3 MI OUT) THE TWR CALLED TO BRASILIA TFC OVER THE NUMBERS AND AGAIN CLRED ME TO LAND ON RWY 16R. I BEGAN AN ABBREVIATED BASE TO FINAL TURN FOR RWY 16R AND AT THAT POINT THE TWR SWITCHED THE RWY CLRNC TO RWY 16L (PRESUMABLY FOR AN EASIER EXIT OFF THE RWY; AS NO ACFT WAS ON A CLOSE FINAL FOR RWY 16L. I ACKNOWLEDGED THE CLRNC. AT THIS POINT; I HAD TURNED FINAL AND WAS OVER THE APCH END OF RWY 16R. I PROCEEDED TO LAND ON RWY 16R. ON THE ROLLOUT AFTER TOUCHDOWN; THE TWR CTLR CAME ON FREQ AND STATED 'NO HARM DONE; JUST WANTED YOU TO KNOW THAT I CLRED YOU FOR THE L AND YOU LANDED ON THE R.' HE CLRED ME TO CROSS RWY 16L AND CONTACT GND CLR OF THE RWY. I CLARIFIED THE INSTRUCTIONS TO CROSS RWY 16L AND ON THE INITIAL CALL TO GND CTL; WAS CLRED TO TAXI TO PARKING. AS I WAS TAXIING TO PARKING; GND CALLED AND STATED 'JUST AS A FRIENDLY REMINDER; THEY'D LIKE YOU TO CALL THE TWR.' I PROCEEDED TO THE GATE AND PHONED THE TWR FROM THERE. AFTER REPLAYING THE TAPES; THE TWR FELT THAT 'PAPERWORK' WOULD BE PROCESSED. AS FOR CONTRIBUTING FACTORS; THE SEA AIRSPACE WAS UNUSUALLY QUIET AT THE TIME OF THE OCCURRENCE. DURING THE MAJORITY OF MY VFR ARRS INTO THE ARPT; TFC HAS BEEN HVY AND REQUIRES FAST MANEUVERING INTO THE FLOW OF IFR ARRS/TFC. THE UNUSUALLY QUIET ATMOSPHERE PERHAPS CONTRIBUTED TO A MORE RELAXED SIT/ ENVIRONMENT WHERE I FELL INTO AN ALMOST AUTOMATED/ROUTINE FLOW OF LNDG ON RWY 16R. HOWEVER; I UNDERSTAND THAT SEATAC; AS OTHER HEAVILY CONGESTED ARPTS (FROM CLASS B'S TO BUSY NON TWRED ARPTS) ARE PARTICULARLY DYNAMIC ENVIRONMENTS WITH MUCH ACTIVITY AND RECOGNIZE THE IMPORTANCE OF CONSTANT VIGILANCE AND ADHERENCE TO ATC CLRNCS. BECAUSE THERE WAS LITTLE TFC; PERHAPS THE TWR CTLR COULD HAVE MADE A CALL TO ME AS HE SAW THE OBVIOUS MISTAKE OCCURRING; INSTRUCTED A GAR TO THE L RWY (RWY 16L) OR PERHAPS COULD HAVE ISSUED ANOTHER CLRNC TO LAND FOR RWY 16R. ULTIMATELY; IT IS THE PIC'S RESPONSIBILITY FOR THE SAFETY OF FLT AND FOR ADHERENCE TO ATC CLRNCS; HOWEVER; PERHAPS COMBINED VIGILANCE FROM ATC AND PLTS ALIKE CAN CONTRIBUTE TO SAFETY IN SUCH SITS. THIS OCCURRENCE HAS REMINDED ME OF THE IMPORTANCE OF CONSTANT VIGILANCE AND OF RESISTING THE HUMAN TRAIT OF 'FALLING INTO PATTERNS' AND HABITS. BUSY AIRSPACE (AS ANY AIRSPACE) REQUIRES ALERTNESS AND A RECOGNITION THAT CLRNCS CAN CHANGE. SAFETY NEEDS TO START AT THE STUDENT PLT LEVEL AND CONTINUE THROUGH RE-EDUCATION AND REMINDERS AS PLTS CONTINUE THROUGH THEIR CAREERS; BE IT VOCATION OR AVOCATION.