Cheeses in Iceland has been very boring since the law just recently changed for the better - we are now able to import a lot of cheeses that we were not allowed to. This happened this year.
The most consumed cheese in Iceland is fresh Gouda.
Another popular one for parties and special occasions is Camembert.
For the longest time, we were not allowed to import any cheese made from unpasteurized milk, but in April that changed.
We are now not allowed to produce cheese from unpasteurized milk or buy unpasteurized milk.
I find this really horrible.
Anyway, we have one cheese that is quite unique to our country, and that is Skyr. Skyr is made from skimmed milk with some special Skyr culture and rennet.
You should be able to find Skyr in the US under the brand name "Siggi's" - http://www.skyr.com/
"Siggi" is a character from the children's show Lazy Town.
We currently have one big cheese producer here in Iceland that owns 99% of the market, one small cheese house (most of their profit seems to come from selling shredded mozzarella in bulk to pizza places) and a couple of small home/farm cheese makers.
So in essence, the cheese market here in Iceland is pretty much just one big company but that will change with consumer awareness and hopefully small creameries.