Around the 15th Century, Ashkenazic Jews (in eastern Europe) developed the challah that we have today. It is thought that the braiding or twisting was a pun on twisting off the little piece of first dough as a reminder of the Temple sacrifices. The braided shape is believed not to be of purely Jewish origin, but modelled after twisted white breads that were found through central Europe and the Slavic countries.
Also, with regard to the strikingly similar zopf:
History of Zopf Recipe
While there has been no recorded history of the bread in particular,
the local legends speak of the origin which happens to be as early as
the 15th century. The custom of the widows cutting off their braids
and burying it with their husbands was replaced with burying the Zopf
which is similar to the braided hair. The custom was followed more in
Bern than in the other parts of Switzerland. However, the bread is
relished all across the country and is considered to be a delicacy.
See also: http://forward.com/articles/2303/south-african-challah/#ixzz3Sn43LrKH
Most potentially problematic halachically (and perhaps, unfortunately, most compelling) is the potential origin recorded by Menachem Mendel:
I mentioned this to my colleague Rabbi Jill Hammer, and she suggested that I look into the connection between ḥallah and goddess worship. Not really knowing what to expect, I found the following in The Woman’s Dictionary of Symbols and Sacred Objects (p. 482):
The braided bread loaves of Germanic tradition were invented by the women of Teutonic tribes, who used to make offerings of their own hair to their Goddess. Eventually they learned to preserve their braids by substituting the imitative loaf, which was called Berchisbrod or Perchisbrod, bread offered to the Goddess Berchta, or Perchta. The name of the braided Sabbath loaf among German Jews, Berches or Barches, was copied from this tradition.
Could it be that those nice braids that my wife makes when she bakes ḥallah really have their source in pagan goddess worship? The linguist Paul Wexler thinks that the original name was actually the German Holle which was the name of a pagan Germanic goddess to whom braided bread was once given in offering. [The German] Holle was replaced at a later date-under the pressure of Judaization-by the [Hebrew] ḥallah, which bore formal and semantic similarity. (See his book The Non-Jewish Origins of the Sephardic Jews, pp. 68-69 and numerous other places in his writings.)
Along the same lines:
Joshua Trachtenberg, in his book, Jewish Magic and Superstition, claims that Ashkenazic Jews in German lands as early as the 10th century adopted the practice of braiding their ritual loaves from their neighbors who worshipped the goddess/spirit Perchta, or Holda, or Holle. According to Trachtenberg, these German women worshiped the goddess by offering their braided hair! The tradition of the times was braiding loaves of bread, called Perchisbrod, as an acknowledgement of this pagan custom. The Jews of German speaking lands may have embraced this local custom, removing from it any hint of its pagan origins!
For more on the religious significance of bread-braiding in antiquity, see: http://en.wikipedia.org/wiki/Pretzel
For those who prefer a less polytheistic origin for the tradition, see: http://www.chabad.org/library/article_cdo/aid/480266/jewish/Why-Is-Challah-Braided.htm
Perhaps the braiding of the challah, which is eaten at the Shabbat table, also represents this idea of unity: how we tie everything together, bringing all the diversity in our lives together for a peaceful harmony and unity that only the Shabbat can achieve.