Answer:
   
   In principle, vegetarianism is compatible with Judaism. In fact, there
   are those who find reasons within Jewish thought supporting
   vegetarianism. However, Judaism categorically rejects the radical
   animal rights position that animals have the same rights as people. It
   should also be kept in mind that, in traditional circles at least,
   vegetarianism may be considered somewhat "strange".
   
   From the traditional viewpoint, vegetarianism for anything other than
   health reasons is not supported, for the following reasons:
   
     * "Ethical Vegetarianism" is rejected because it is G-d who allows
       us to eat animals. The laws of shechita (ritual slaughter) are
       designed to provide a compassionate way to kill the animals for
       eating.
     * Eating animals actually elevates the animal. In traditional
       thought, animals can only do so much. When a jew makes a blessing,
       eats animal products, and then uses that energy to do mitzvos,
       (s)he is elevating the animal to G-dliness in a way that the
       animal could not do itself. This is considered to be a holy
       endeavor, and is further detailed in the concepts of chassidus.
     * The torah states that "eating meat and drinking wine give a man
       pleasure." All festive and holiday meals have both components:
       they bring us gladness and enhance our simcha. One approach to
       addressing this is to save eating animal products for Shabbat and
       holidays, and eat pareve during the week.
       
   Non-traditional movements do hold with the notion of "Ethcial
   Kashrut". Gates of Mitzvah, the Reform guide to Mitzvot, notes: "One
   might opt to eat only kosher meat or even to adopt some form of
   vegetarianism so as to avoid the necessity of taking a life. (This
   would be in consonance with the principle of tsa-ar baalei
   chayim--prevention of cruelty to animals.)"
   
   According to most halachic authorities, when the Temple is rebuilt,
   all Jewish men will be obligated to partake of the paschal lamb with
   their families. Nothing short of a severe lamb allergy permits
   abstaining from this sacrificial meal (of course, it is believed that
   when the Temple is built, G-d will heal the sick, so the allergies
   will go away). There are various positions on this issue, which have
   been written about in Kashrus magazine and on the net. Consult your
   local rabbi for details.
   
   Note that, while Judaism defines animals as below humans and does not
   give animals the same rights as people, it does take very strong
   pro-animal stance. Animals must be treated with care and respect;
   recall that the Torah says that a hungry animal must be fed before its
   master.