Answer:
     * Orthodoxy: Traditional Jewish law is that if a child dies before
       reaching the age of 30 days, no formal burial is required. Such a
       child is considered a nefel, and for such a child, no burial and
       no mourning rites are required (Ket. 20b; Shab. 135b; Evel Rabati
       I; etc.) The Shulhan Arukah addresses whether a eulogy is
       permitted; it says for the children of the poor, it may be done
       from the age of five and onward; and for the children of the rich,
       from six and onward (M.K. 24b; Shulhan Arukh 344.4). This shows
       that, traditionally, little was made of infant deaths. Further, a
       nefel was treated as an amputated limb, and buried in the general
       section of the cemetary (Ket. 20b) to avoid ritual uncleanliness
       for the priests (M. Edut 6.3; Yad Hil. Tumat Hamet 2.3; Pahad
       Yitzhaq, Ever). Note that, strictly speaking, it was not necessary
       to bury amputated limbs (Shulhan Arukh, Yoreh Deah #209).
       It's very easy to think of the traditional position as
       "heartless." When you've lost a baby and need to grieve, it's
       natural that you'd want to do it in the way you're familiar with.
       Orthodox families in this situation are usually forced to look for
       alternative ways of coming to terms with their grief, since in
       most cases, the traditional funeral and mourning periods are not
       observed. This doesn't mean that nothing has happened, or that as
       far as Judaism is concerned, they have not experienced a loss.
       They still need consolation and any compassionate Orthodox rabbi
       and community will recognize this and do their utmost to help the
       family through their time of pain.
     * Conservative: Four papers have been validated by the Conservative
       movement's Commitee on Jewish law and Standards on this issue.
       Conservative Judaism affirms that where Jewish law allows for more
       than one possible position, a congregation should follow the
       ruling of its rabbi, who as mara d'atra [halakhic authority] has
       the sole responsibility and authority in his/her community for
       making a p'sak [ruling/decision]. The significant teshuvot are
       summarized below:
         1. Rabbi Isidoro Aizenberg, 1987. (a) When a full-grown,
            full-term baby dies within 30 days after birth, there is
            aniut, keriah, burial, shivah and shiloshim; no eulogy is
            delivered and the burial is peformed by the immediate family
            members. If the parents wish, they may recite the kaddish for
            30 days. (b) If the baby was born prematurely, the above
            customs should be practiced only if it died more than 30 days
            after its birth. (c) If the baby was born prematurely and
            died before 30 days are over, the baby should be treated as a
            fetus. There is burial, but no other rituals are practiced.
            In all 3 cases, should parents ask the rabbi if they may
            recite the kaddish, their request should not be denied. This
            teshuva can obtained from the CJLS by one's local
            Conservative rabbi. (II)
         2. Rabbi Debra Reed Blank - teshuva on miscarriage. She agrees
            with the first teshuva for the case of a full-term baby dying
            within 30 days after birth. For cases when the fetus was not
            born alive, full mourning rites are not called for or
            appropriate, for that would compromise the position of
            classical Judaism on the legitimacy of abortion in some
            circumstances. However, in event of a miscarriage the
            community should tend to both members of the couple under the
            rubric of bikur holim (visiting the sick), for they are
            suffering from the loss of the child that they were expecting
            to have. The couple may recite the kaddish if they choose.
            This teshuva can obtained from the CJLS by one's local
            Conservative rabbi.
         3. Rabbi Stephanie Dickstein, 1999. In an extension and revision
            of her 1992 paper, she also agrees with the first teshuva for
            the case of a full-term baby dying within 30 days after
            birth. For cases when the fetus was not born alive, she holds
            that burial in a Jewish cemetery is required for stillbirths,
            and she recommends a funeral service. The stillborn may be
            named and circumcision can, but need not, be done. The grave
            should be marked later. After the first day, the parents may
            observe the practices associated with shiva b'tzniut (private
            observances which do not involve the community). This teshuva
            is online at
            [5]http://learn.jtsa.edu/topics/diduknow/responsa/hatesh_conf
            ront.shtml
       Additionally, Conservative/Liberal Jewish responses to these
       situations can be found in Nina Beth Cardin's "Tears of Sorrow,
       Seeds of Hope: A Jewish Spiritual Companion for Infertility and
       Pregnancy Loss" (Woodstock, VT: Jewish Lights, 1999).
     * Reform: Reform believes that times have changed from the days of
       the large family and common infant deaths of tradition. This has
       made all events in a child's life more significant and magnified.
       Thsi includes the tragic death of a yong child, a still-birth, or
       a miscarriage. A responsa issued in 1983 (Contemporary American
       Reform Responsa #106) suggests that there be a simple burial for a
       still-born infant or a child who dies at an early age. This
       provides a way for the family to overcome its grief. It indicates
       that a miscarriage may, however, be disposed of by the hospital or
       clinic in accordance with its usual procedures. Not burial is
       necessary in such a case, but it is not prohibited either. They do
       suggest burial for infants, and possibly for still-births.
       Personal autonomy allows laypeople and rabbis to observe or not
       observe as they see fit.