List of airlines that fly to Iceland all year round:


Icelandair

Icelandair maintains regular scheduled flights to Iceland from the following cities:
All year:
Amsterdam, Boston, Copenhagen,  Denver, Frankfurt, Glasgow, Helsinki, London, Manchester, Oslo, Paris, Stockholm, New York, Seattle and Washington.
Seasonal:  Alicante, Barcelona, Bergen, Berlin, Billund, Brussels, Gothenburg, Orlando, Halifax, Hamburg, Madrid, Milan, Minneapolis / St. Paul, Munich, Stavanger, Toronto, Trondheim
Book online with Icelandair

Iceland Express

Iceland Express maintains regular scheduled flights to Iceland from the following cities:
All year: London (Gatwick airport), Copenhagen, Berlin and Warsaw.

Seasonal: Alicante, Barcelona, Basel, Billund, Bologna, Frankfurt (Hahn airport), Gothenburg, Krakau and Paris.
Book online with Iceland Express

WOW air

WOW air maintains regular scheduled flights to Iceland from the following cities:
Operates from June 1st: Alicante, Basel, Berlin (Brandenburg), Cologne Bonn, Copenhagen, London (Stansted) Krakow, Paris, Lyon, Stuttgart, Zurich, Warsaw.                     
Book online with WOW air

easyJet

Maintains seasonal flights to Iceland from London from March to October.
Book online with easyJet

Approximate flight times from several cities:

Copenhagen, London, Frankfurt, Paris, Amsterdam to Reykjavik... approx: 3 hrs
New York, Boston, Minneapolis to Reykjavik... approx: 5-6 hrs