I use the term "claim" in the widest sense; I have included any ethnicity that has been rumored to be part of our ancestral heritage. Here is the full list, sorted by grandparent:
Note that in spite of their long and strong connection to Norway, my mother's family does not identify as purely European in origin. In addition to Norwegians and Russians, family tradition tells us that we also have ancestors from Asia; more specifically, Mongols and Romani people (the latter having originated in India and mixed with many different groups along the way to - and within - Europe). The Mongol bit is something I only recently got confirmed as a real family story, and I find it extremely fascinating, especially since I've always loved Mongolian music.
Comparing claims and DNA
Let's do an experiment. If we go by family tradition only, I should be of Norwegian, Swedish, English, Russian, Mongol and Romani descent. Does this fit with my DNA results?
Of course, many additional ancestral ethnicities have been uncovered through genealogical research, and some of them show up in my DNA results. I have Denmark as a Recent Ancestor Location at 23andMe, as well as Finnish and Southern European percentages. These results are fully consistent with my paper trail (Danes and Forest Finns in the 1600s and 1700s, and Italians in the 1500s). In addition, my Y-DNA has unveiled Scottish ancestry from the 1600s on my direct paternal line. This shows that my family members' knowledge was not complete, and that parts of our ancestral heritage were in fact forgotten during the course of time. I find it particularly noteworthy that nobody in my family had any knowledge of Forest Finn ancestry before I started researching, even though at least three of my great-grandparents are of traceable Forest Finn descent.
Any DNA from the additional ancestral ethnicities I have uncovered - notably our West African ancestry - has been "washed out" and is not visible in my results. It is, however, visible in the results of older generations of my family. Those older generations also have other mysterious admixtures which I hope, one day, to get to the bottom of.