Ingredients: Icelandic local specials
Being a treeless island with a harsh climate, there are few natural ingredients that are specific to Iceland that are not available on mainland Europe.  Some exceptions include puffin and whale meat, however, it is likely illegal to import those into your home country.  Iceland does have some amazing quality lamb and dairy goods (e.g., skyr), however, it might also be difficult to take those home.  With that said, there are a number of prepared foods that are unique to Iceland and are difficult to find elsewhere:


Hákarl: dried putrified shark;
Harðfiskur: dried fish;
Brennivín: liquor, similar to akvavit; and
Tópas and Opal: licorice/menthol liquors.


The makers of Opal also make a candy of the same name that tastes just like the liquor.  It's great for getting the children hooked on the flavor from a young age ;-)

While you are in Reykjavík, make sure to get some hot dogs at Bæjarins Beztu Pylsur; they are perhaps the best I have had anywhere in the world.  I am not sure if they sell their raw sausages, but if they do, that would definitely be something I would want to take home if I were there again.