You can try different nvidia drivers to see if the tearing goes away. You are also using a 60Hz monitor so going over 60fps can cause tearing from your monitor not being able to keep up with your graphics. My advice is to keep your vsync on ;P
Keep Vsync on. It's purpose is to keep your frame rate constant and help reduce screen tearing, amount other things. If you can't get 60FPS in every game, lower your graphic settings. A GTX580 won't run every modern game maxed out at 1080.