If you're reading this, you don't mind Game of Thrones spoilers.

Yes, white walkers can be killed.

Elisabeth Garber-Paul explains how to kill a white walker:

1. Make sure you’re dealing with a White Walker (and not your garden-variety wight).*

*White Walkers are supernatural beings typically seen riding dead horses, mammoths, or ice-spiders. They have white hands and speak in screams. Wights are humans killed by White Walkers and serve as their minions. They have rotting flesh and are clumsy.

2. If dealing with a wight, set it on fire. If no flame can be found, hack off its limbs with a sharp weapon. This may not always kill them, but it’ll debilitate them long enough for you to seek safety behind the Wall.

3. If facing a White Walker, obtain a dragonglass dagger. Deposits of dragonglass (also known as obsidian) can be found on the island of Dragonstone or the port city of Asshai.

4. Stab. Any White Walker flesh that comes in contact with dragonglass will smoke and melt away into a puddle. But beware: White Walkers are quick and have weapons of sharpened crystal. If they kill you, you might come back a wight.

More about White Walkers from the Game of Thrones television series:

http://gameofthrones.wikia.com/wiki/White_Walkers

More about "The Others" from the Game of Thrones books:

http://awoiaf.westeros.org/index.php/Others

What is the difference between a Wight and an Other?

http://scifi.stackexchange.com/questions/12065/in-asoiaf-what-is-the-difference-between-a-wight-and-an-other

Why are the people of Westeros so afraid of White Walkers?

http://scifi.stackexchange.com/questions/33804/why-are-the-people-in-westeros-so-afraid-of-the-white-walkers

And why didn't the White Walkers kill Sam at the end of season 2 of Game of Thrones?

We'll have to wait to find out the answer to that!