Most people, whether or not they know his name, will at least be familiar with his work for the first Alien film--primarily the design of the original xenomorph and the sets used for the alien derelict spacecraft. The imagery has aged well compared to so many other horror films. As much as Alien is Ridley Scott's film, it is also Giger's, because it wouldn't be the same film without the unique look he created.
Of course Alien is just the tip of the iceberg that is his body of work. He created countless images, often disturbing and controversial. He was known for his distinct fusion of organic and mechanical elements.