The local currency is the Icelandic króna ISK, and its value collapsed quite dramatically during the 2008 economic crisis. As of Aug 2012, it trades at around 1 EUR = 150 ISK. This has also made local prices more affordable for the visitor, although the prices of imported goods have risen rapidly.
You will get a better rate of exchange if you buy and sell your króna in Iceland itself. Just about every establishment in Iceland will accept a credit card, including taxis, gas stations, souvenir stands, and even the most remote guest house, so it is not necessary to carry large amounts of Icelandic currency. However, due to the currency's instability some credit cards are still wary of króna transactions, so check with your bank before you go and don't rely entirely on plastic.
Following the 2008 economic crisis, foreign trading in the króna has been restricted, so you may struggle to get króna notes in your home country. As at March 2009 we found the only method was to find old stock at Bureaux de Change which carried it in stock, such as Marks & Spencer. This may have to be ordered in about a week in advance though.
shopping
Typical Icelandic products that make good souvenirs include:
Icelandic wool products. Icelandic sheep are a unique breed that produce a soft and durable wool, and Icelandic woolen goods hats, gloves etc. are soft and warm; don't just buy them for other people if you plan to visit the interior.
Arts and crafts. Iceland has a huge number of great little craft shops that sell everything from musical baskets and wonderful weird porcelain sculptures to paintings, glasswork, and jewelery. An interesting note is that the National Galleries tend to carry the same artist's work in the gift shops rather than the usual mass-marketed products found in so many other museums.
Local music. There is a plethora of interesting local music CDs beyond just Björk and Sigur Rós worth hunting for. Obscurities worth picking up include Eberg (http://www.eberg.net), Hera (http://www.herasings.com), Retro Stefson, FM Belfast, Worm is Green, Múm, Singapore Sling, and Bellatrix. Be warned that many of these CDs are often available back home as imports for much lower prices. CDs tend to cost 1500 to 2000 Kr.