PVT PLT IN A PA28-200 PERFORMS AN APCH TO WRONG RWY; OPPOSITE DIRECTION TFC. HAS TO GO AROUND TO AVOID OTHER ACFT ON TKOF; CLB.

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RETURNING TO GEU FROM PRC; CONTACTED GEU TWR (121.0) AND RPTED 10 MI N OVER SUN CITY; 2500 FT INBOUND; LNDG. TWR INSTRUCTED TO 'RPT OVER PWR PLANT.' UPON REACHING PWR PLANT; TWR ADVISED TO TURN SBOUND; ENTER L DOWNWIND RWY 19. I PROCEEDED AS ABOVE; RPTED L DOWNWIND ENTRY ABEAM THE TWR. MY MISTAKE WAS I HAD ENTERED R DOWNWIND RWY 1. TWR 'CLRED TO LAND RWY 19.' I BEGAN SETTING UP LNDG CONFIGN RWY 1. PROCEEDED TO FLY THIS TO FINAL FOR RWY 1 TO WITHIN 1 MI AND APPROX 350 FT AGL. TFC SIMULTANEOUSLY DEPARTING RWY 19 RADIOED TWR AND INQUIRED ABOUT THE ACFT MANEUVERING OFF THE APCH END OF RWY 1. TWR CONTACTED ME AT THE SAME TIME I MADE VISUAL CONTACT WITH THE DEPARTING ACFT; REQUESTING MY POS. (I REALIZED MY GRAVE ERROR AT THIS POINT.) AT TWR REQUEST I IMMEDIATELY INITIATED A CLBING L TURN. DEPARTING TFC WAS AT LEAST 200 FT ABOVE AND 1000 FT HORIZ -- NO COLLISION WAS IMMINENT. I MANEUVERED TO A R DOWNWIND FOR RWY 19 AND LANDED UNEVENTFULLY. 2 THINGS CONTRIBUTED TO THIS -- FATIGUE AND COMPLACENCY. GENERALLY; WHEN INCOMING FROM THE N; I HAD BEEN CLRED STRAIGHT-IN FOR RWY 19. SINCE I WAS ASKED TO PROCEED TO THE PWR PLANT; I ASSUMED RWY 1 IN USE. I WAS 'CLRED' TO THE PWR PLANT FOR SPACING! FATIGUE CONTRIBUTED TO MY COMPLACENCY. THE GOOD THINGS -- NOBODY HURT; I LEARNED A GREAT DEAL; I WON'T MAKE THIS MISTAKE AGAIN.