Dragons and Treasure

I was talking with a friend about the various books we have read and it came to our attention that dragons are almost always connected to treasure and/or greed.

Take for instance Smaug, the dragon from Voyage of the Dawn Treader and various other stories. Draco from DragonHeart seems to be one of the few that doesn't follow this rule.

So my question is, where do you think this got started from? Is there some basis from mythology that I am missing perhaps?