Judaism - Ethnicity
Judaism, while not unique in the modern world, is still something of an anomaly when it comes to the definition of a religion.
The norm in the ancient world (in Asia until Buddhism started spreading, in Europe until Christianity became independant of the Roman empire and in Africa and the Americas until Christianity took over) was that religion was completely integrated with culture, ancestry, nationality, political structure and geographical location. Confucianism still shows many of these mixes, as does each particular variety of Hinduism, Zoroastrianism, Native American spiritualism and many others. Since Judaism began as such a religion / culture / nation / race mix, it retains aspects of all of these into the modern world. Jews being exiled from their homeland forced them to develop a strong cultural bond and a certain amount of isolationism within their homes-in-exile. This mild xenophobia means that Judaism cannot have as loose a definition as, say, members of some particular Hindu varieties, nor can one's "Jewishness" be tied primarily to a place or a particular ancestor. Since Judaism allows conversions, one's "Jewishness" cannot solely be considered in terms of one's heritage either, as it can with Zoroastrians. Since Judaism has no desire to be universally applied, it cannot be solely a matter of choice either, as it is with Christianity and Buddhism - one can choose to join Judaism but still needs verification and acceptance by the existing Jewish body (I.e. conversion) before they can truly say they are Jewish.
Ultimately, I would say that modern Judaism more resembles a well-knit association of cultures than it does an ethnicity or a religion.