Answer:
   
   There are many explanations:
     * One explanation is that the word kike originates from the word
       "keikl", in Yiddish, which means "circle". At Ellis Island, one of
       the main immigration checkin points, immigrants were intially
       grouped by religion and language in order to make it easier for
       them to communicate with each other and also to be identified more
       quickly by waiting relatives there to meet them. Christians were
       marked off with an 'X' which was likely really supposed to be a
       cross; Jews were marked with a circle which was really likely
       supposed to be the Star of David. It is easy to see how the staff
       could become sloppy at drawing these symbols as 'x' and 'o'. The
       word "keikl" was used by the Jews making fun of the poorly drawn
       star; they referred to each other as being 'circles'.
       Unfortunately, from this innocent usage, the term aquired a
       derogatory meaning.
       Robert L. Chapman's "American Slang" has a slight variation on the
       above. Rather than saying the circle was a mark made by the staff
       to symbolize the Star-of-David, the book says: "Jews who could not
       sign their names would make a circle." This suggests that it was
       Jews themselves who started using the circle- presumably to avoid
       the X which was reminiscent of a cross.
     * According to "Our Crowd", by Stephen Birmingham, the term kike was
       actually coined as a putdown by assimilated American German Jews
       for their Eastrern-European bretheren: "Because many Russian
       [Jewish] names ended in 'ki', they were called 'kikes'- a German
       Jewish contribution to the American vernacular. (Germans are also
       said to have invented the term "Bohunk", referring to Jews from
       Bohemia.)". Following this explanation, the name kike was
       deliberately coined to put-down Jews- but only a certain subset of
       Jews. The name then proceeded to be co-opted by Gentiles and used
       against all Jews in general.
     * Robert L. Chapman's "American Slang" also notes that the word
       could be a reference to "Ike", a nickname for Isaac.
       
   [Thanks to Andrew Nusbaum for bringing some of the alternate
   explanations to my attention.]