Icelandair has 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.
Book online with Icelandair here (select your point of departure on the main page)

Iceland Express offers regular scheduled flights to Iceland from the following cities:
All year: London/Stansted, London/Gatwick, Copenhagen, Alicante, Berlin and Warsaw.
Winter (selected dates): Friedrichshafen.
Summer: Barcelona, Basel, Billund, Eindhoven, Frankfurt/Hahn, Friedrichshafen, Gothenburg, Paris, Stockholm.
Iceland Express also operates flights (summertime only) between Copenhagen and Akureyri, North Iceland.
Book online with Iceland Express here

Scandinavian Airlines System has regular scheduled flights to Iceland from Oslo.
Book online with SAS here

This Faroese shipping line sails to Seyðisfjørður on the east coast of Iceland from Hanstholm (DK), Bergen (NO) and Scrapster (UK).
Book online here
If you need to find out more about domestic transport, please go to this page on visiticeland.com