Iceland was invaded and occupied by the UK (the US took over the occupation a year later) during WWII.

With the exception of slave raids (for example, the Turkish abductions), clashes between German and English fishermen with Danish administrators on Icelandic soil, and Jørgen the Dog-Days King's temporary seizure of power in Iceland, there have not been any attempts to invade Iceland. There is no evidence of any concrete plans by Nazi-Germany to invade the island prior to the British occupation in WWII. The Nazis examined the feasibility of seizing the island from the British but found it unfeasible. There is no evidence of Soviet intentions to invade Iceland during the Cold War. There is no evidence of German intentions to invade Iceland during WWI (the British didn't think so either, which explains why they didn't invade Iceland).

Iceland had little of value for much of history. Danish kings tried at different times to sell Iceland to the Scottish King, English King and German merchants but nothing came out of these attempts. (I'm not completely familiar with this episode but I believe Sweden decided against obtaining Iceland in negotiations concluding the Napoleonic Wars). A British businessman tried to convince the British government to purchase Iceland towards the end of the 18th century (he wanted to mine the sulphur) but the government wasn't interested. Secretary of State Wiliam Seward considered purchasing both Greenland and Iceland in the 1860s. A US Senator talked openly about annexing Iceland towards the end of WWII but that was never a realistic option.

Edit: Sources:

• Agnarsdottir, Anna. (1992). Scottish plans for the annexation of Iceland 1785–1813. The Scottish Society for Northern Studies, 29, 82–96.
• Ingimundarson, Valur. 1996. Í eldlínu kalda stríðsins. Reykjavík: Vaka-Helgafell.
• Ingimundarson, Valur. (2011). The Rebellious Ally. Dordrecht: Republic of Letters Publishing.
• Jensdottir, Sólrún B. (1986). Anglo-Icelandic relations during the first world war. New York: Garland.
• Karlsson, Gunnar. (2000). The History of Iceland. University of Minnesota Press.
• Thorsteinsson, Björn. (1961). Henry VIII and Iceland in Saga Book of the Viking Society,1957–61, 67–101. London: University College.
• Thorsteinsson, Björn. (1976). Tíu Þorskastríð 1415-1976.
• Thor Whitehead's books and articles on Iceland during WWII.