I am ashamed to admit that all this time -- I've been in a dilemma about which continent Greenland is a part of! Is it North America or is it Europe?

I took a look at my atlas (Orient-Longman) today; it shows Greenland along with the maps of North America.

Also, from what I see, the distance between Greenland and one of Canada's northern-most islands (Ellesmere Island) seems like just 20-30-odd kilometres! On the other hand Iceland (Europe) appears to be at least 500 kilometres away!

However, Greenland, being a part of Denmark should be classified as a part of Europe. (Or should it? Even though it's a big hunk of land, should it be treated like other dependent territories?)

What does everyone else think? What is the more established classification?

I think it depends on the context in which we're looking at Greenland.

From the point of view of physical geography, it's obviously part of North America.

Political geography, in its strict sense, would regard Greenland as part of North America that belongs to a European country (in the same way as Ceuta and Melilla are geographically in Africa but are politically part of Spain).

But when you move away from strict geography things get complicated. If you want to calculate the gross domestic product of Europe, you will probably include Greenland as part of Denmark and hence as part of Europe. And in the world of football, Greenland is aiming to join UEFA (the European football federation) and not CONCACAF (the North and Central American one).

According to this site: http://capitals.com/geos/gl.html#Geo Greenland is an island which dominates the North Atlantic Ocean between North America and Europe. It's also the world's largest non-continental island. (And here, I thought Australia was)
It's self-governing, but foreign affairs are controlled by Denmark. Since it's about 81% ice-capped, Greenlanders are not likely to see many tourists.