Answer:
   
   Judaism does have a role that is sometimes referred to as
   "Godparents", but this is not "Godparent" in the Christian sense. In
   America, Jews began picking up words used by non-jews, but gave them
   Jewish meanings. In Judaism, a person nowadays referred to as a
   "Godparent" actually has a different job. This person is really called
   the Sandek (Hebrew term), Ba'al berit milah (Hebrew term) or the
   Kvater (Yiddish term). Among some Sephardi communities it is customary
   for the Sandek (who holds the child during the brit) to buy the
   clothing, blankets and diapers for the baby. In all communities, to
   act as sandak is considered a great honor and as a meritorious
   religious act which, according to the kabbalists, has atoning
   qualities. Where a grandfather of the child is still alive, it is
   customary to bestow the honor of sandak upon him. The woman who brings
   the child to the circumcision and hands it over to the sandak is
   called sandakit.
   
   The Sandek is obligated to see to the child's upbringing if the
   parents fail or are unable to do so -- just like a godparent. Note
   that the sandek really should be Jewish. However, this practice is not
   a universal minhag (custom), and since it is not universal, it doesn't
   have the status of law. Thus, technically speaking, one could make a
   decision that a gentile may act as Sandek. In practice, most rabbis
   and mohelim (people who do the circumcision) won't allow this, but
   some will.
   
   The notion of Godparent in the western sense is not a Jewish notion;
   it is derived from the Christian godparent, whose charge is to ensure
   the child's spritual upbringing in the church. Judaism rejects this
   concept outright.
   
   In the Jewish tradition, there are two tiers of responsibility: the
   immediate family, and the local Jewish community. Jewish law, from the
   Talmud itself, absolutely mandates that the parents of a child are
   obligated to teach the child three things:
    1. An education that can lead to a trade, so that the child can have
       a career.
    2. A comprehensive Jewish education.
    3. How to swim.
       
   These three obligations are an absolute minimum. The second tier of
   responsibility falls on the Jewish community that the parents live in,
   which is obligated to work together to set up a Beit Midrash (house of
   study, including a Hebrew school), hire teachers (preferably,
   including at least one rabbi, as well as other learned lay-people), to
   build a mikveh (to allow families to observe the laws of family
   purity, allow people to convert to Judaism, and a number of thing
   things as well), and finally, to build a synagogue.