You were warned about it almost from the day you started riding motorcycles. You've talked to riders it has happened to. But you never expected to find yourself where you are now, speeding toward a car that is inexplicably turning left in front of you, its driver staring wide-eyed at you through the window but not stopping. In a flash you think, Holy hell. This is really happening.
What's the best way to avoid this nightmare scenario? Awareness is your best defense. Remain vigilant in traffic and position yourself for the best view of opposing traffic and left-turn lanes. Avoid riding where another car blocks your view because that car is also keeping you from being seen by the turning driver. Always be aware of your surroundings so that you can decide quickly if you have more room to swerve left or right, though the odds are more in your favor if you shift into traffic moving in your direction than steering into oncoming cars.
Prepare to avoid. Your best bet is to plot an escape path and begin executing it as soon as you recognize the threat from the left-turner. This is always difficult and highly variable. Did the driver see you and stop? In that case, look for the hole ahead of the car and aim for it. But beware that the driver still might not see you and is only stopping based on some other stimulus. He or she could start up again and take a second shot at you. Did the driver keep going? Then your best bet is to steer around the back of the car, trying to avoid ending up across the centerline. Keep your eyes on the escape route; if you continue to look at the car, you're likely to hit it. And be prepared to change your plan based on the actions of the driver.
Even so, when in traffic it's important to cover both brakes and be prepared to use them right to the verge of lockup or into ABS activation if your bike is so equipped. The object is to avoid the accident—not hit the car at a lower speed. (Though, truthfully, that might be all you can hope for.)
Beware the fresh green light. If the light just turned green for you, it might have just turned red for the oncoming left-turn lane. A driver trying to beat the red could come hauling across your path, scrambling all the traffic in the intersection. Don't get caught in the middle of it.