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
List of airlines that fly to Iceland all year round:
Icelandair
Icelandair maintains regular scheduled flights to Iceland from the following cities:
All year: London, Glasgow, Copenhagen, Manchester, Oslo, Paris, Stockholm, Amsterdam, Frankfurt, Boston, Minneapolis, New York, Orlando and Toronto (seasonal).
Summertime only: Barcelona, Bergen, Berlin, Gothenburg, Halifax, Helsinki, Madrid, Milan and Munich.
Iceland Express 
Iceland Express maintains regular scheduled flights to Iceland from the following cities:
All year: London (Stansted airport and Gatwick airport), Copenhagen, Alicante, Berlin and Warsaw.
Winter (selected dates): Friedrichshafen.
Summer: Barcelona, Basel, Billund, Eindhoven, Frankfurt (Hahn airport), Friedrichshafen, Gothenburg, Paris, Stockholm.
Iceland Express also operates flights (summer-time only) between Copenhagen
and Akureyri, North-Iceland.
SAS Maintains regular scheduled flights to Iceland from Oslo.