Icelandic cuisine has changed a lot in the last few decades from involving mainly lamb or fish in some form or other, as the popularity of other types of food has increased. A vegetarian diet is more tricky to maintain but there are several vegetarian restaurants in Reykjavík and vegetarian dishes widely available at other restaurants.
Distinctively Icelandic foods include:
harðfiskur, dried fish pieces eaten as a snack with butter also good with coleslaw
skyr, a yoghurt-like dairy product available in flavoured and unflavoured varieties all over the country. Low in fat and high in protein.
hangikjöt, smoked lamb
svið, singed sheep's head
Slátur, consists of lifrarpylsa, a sausage made from the offal of sheep, and blóðmör which is similar to lyfrapylsa only with the sheep's blood mixed into it.
Iceland is famous for its whale meat, and is one of the few places in the world where it is possible to eat Minke whale. The common assumption is that whale meat is a traditional dish in Iceland, and while it is available in restaurants this is generally for the tourist experience. Whaling has long been a tradition in Iceland, albeit it has become a controversial issue in recent times. However, most restaurants that cater to tourists will sell whale meat, and if you are feeling a little more adventurous some places will serve grated puffin with it if you ask.
During the Þorri season late January-Early February many Icelanders enjoy Þorramatur, a selection of traditional Icelandic cuisine which usually contain the following: hákarl putrefied shark cubes, Sviðasulta brawn [head cheese] made from svið, Lundabaggi Sheep's fat and hrútspungar pickled ram's testicles. Þorramatur is usually served at gatherings known as Þorrablót. If you find yourself invited to a Þorrablót do not be afraid to politely refuse some of the more unpalatable delicacies, as many Icelanders chose to do so as well. Don't worry about going hungry, though, as many of the more "normal" foods mentioned above are almost always available too. If uncertain which is which, do not be afraid to ask the caterers for assistance.
A similar event to Þorrablót is Þorláksmessa, celebrated on 23 December each year. During this day you might find yourself invited to skötuveislur where cured skate is served. As with Þorrablót, you can politely refuse to partake in the skate other type of fish is usually served alongside it for the less adventurous. A word of warning though, the pungent smell that accompanies the cooking of cured skate is very strong and sticks to hair and clothing very easily. Do not wear formal expensive clothing at these gatherings, especially not clothing you intend to wear during Christmas.
Any Icelanders' first choice of fast food is usually the pylsa or hot dog. It is usually served with a choice of fried onions, fresh onions, ketchup, mustard and remoulade. It is cheap compared with other fast food staples at around 250 kr, and is sold in every one of the small convenience stores/eateries/video rentals/sweet shops that litter Icelandic towns.
Food prices are particularly high in Iceland - the following sample prices were accurate as of summer 2012:
ISK 800 - 2000 for a hamburger.
ISK 250 - 400 for a hotdog
ISK 3000 - 8000 for a three-course meal in a restaurant.