The roll with a hole is of course one of the iconic Jewish foods. Brought from Eastern Europe around the turn of the century, its presence in English was first noted in 1919. The word comes from Yiddish beygl, sometimes written beigel, from Middle High German boug, meaning "ring, bracelet" and related to the Old High German biogan "to bend" and the Old English beag, meaning "ring." According to New York Times columnist William Safire, the Yiddish beigel was shortened and anglicised to bagel around 1932.
This etymological insight sheds light on a vexatious and long-running communal schism within Anglo-Jewry - whether the first syllable should properly be pronounced like the first syllable in bicycle or like that in bay. The Yiddish spelling of beigel should make clear once and for all that the former is the older and more authentic pronunciation (though I confess that I use the latter pronunciation and I'm not about to change).
In Israel you will find something called a bageleh literally a little bagel. This really doesn't look much like a bagel at all; the hole is too big, the dough is too soft, and it is covered in sesame seeds. Yet the etymology is obviously the same. The Hebrew language blog Balashon explains that the similarity is in the cooking process. And so Israel and the diaspora drift apart yet still retain deep common bonds.