Answer:
   
   Judaism does not practice female circumcision. However, there are many
   traditions that have arise related to the birth of a girl:
   
     * Commonly, girls are welcomed into the convanent through a naming
       ceremony, held in the synagogue.
     * Among Bucharan Jews when the father of the newborn girl is called
       to the Torah for the naming the congregation sing the song "Dror
       Ykra L'ven im Bat" in which each line ends with the word "bat".
       After the reading of the portion and the naming, candies are
       showered on the father and the congregation calls "Mazal Tov".
     * Many Sephardim have a party where they repeat the naming. A Cohen
       is invited and he holds the baby and blesses her with the "Birkat
       Cohanim". Fruit which Israel was blessed for them are served, and
       the Rabbi of the community holds the baby girl on his knees and
       says the words from the Song of Songs "Yonati Bechagvei Haselah"
       (2:14): The ceremony is called "Zeved Ha'bat". The word Zeved
       means gift and comes from Berayshit 30:20 where Leah said at the
       birth of Zevulun "Hashem gave me a good present" and then she gave
       birth to Dina.
       
   The more liberal movements have developed other ceremonies. There is
   [5]an excellent book on the subject by Anita Diamant. Another good
   reference is Lifecycles Volume 1 : Jewish Women on Life Passages and
   Personal Milestones, which includes material from Reform,
   Conservative, Orthodox and Reconstructionist contributors. It was
   edited by Debra Orenstein, and is available from Jewish Lights
   Publications in Vermont.
   
   The Simchat Bat/ Brit Bat / Brit HaHayim is increasingly appearing in
   Modern Orthodoxy has well. A Simchat Bat ceremony is now in the
   Rabbinical Council of America's [Orthodox] Rabbi's manual. This
   ceremony is based on traditional Jewish forms.
   
   The Rabbinical Assembly [Conservative] has included the Simchat Bat
   rite in its new rabbi's manual. As the ceremony is still evolving, the
   RA's manual presents, within a common religious ceremony, three
   options that parents may choose to perform: (A) Lighting seven candles
   (symbolizing the seven days of creation) and holding the baby towards
   them; (B) Wrapping the baby in the four corners of a tallit; (C)
   Lifting the baby and touching her hands to a Torah scroll. A detailed
   article on this topic can be found at:
   [6]http://www.bnaibrith.org/ijm/articles/thnkhvn/.