Iceland is very advanced in all technology. It even aimed to be the first country in the world to have only plastic money (cards of all kinds).
Most common are VISA and MASTERCARD. Many vendors skip adding more credit card brands because of high commission rates. Other common cards would be: AMEX, JCB, Diners Club, Discover, Union Pay.
USEFUL TIPS
Make sure your card is not going to expire during the trip
Make sure there is enough money, funds on your card. F.e. if you are renting a vehicle the lessee could withhold a self risk automatically lowering your reserves on the card.
Make sure you have a 4 digit PIN. Many self served gas stations only work with 4 digits or less. A workaround would be to buy gasoline cards at a served gas station