I know a few people who are ostensibly Orthodox but who are also vegetarian. An interesting combination. Some of these are silly highschool girls who say they are vegetarians but really just don’t like the taste of meat or want to eat less in their speeding race to anorexia. But I also know some serious vegetarians and at least one family who are strictly vegetarian.
In general, being an Orthodox vegetarian Jew doesn't pose too many problems for daily life since there aren’t really any halachot that say a person _must_ eat meat. You don't _have_ to enjoy meat on holidays and Shabbos even though that is a strong custom. And we don't eat the korban Pesach lately, though the fact that we once did indicates a strong contradiction between the values of vegetarians and the implied values of Orthodoxy. Orthodoxy typically sees korbanot as good things and that it is a damn shame that we can’t have them today. Certainly in the Torah, God sees them as good things since he commands them to be given so often.
Ok, but besides the philosophical differences between normative Orthodoxy and vegetarian values, there is a real physical issue with vegetarians in relation to Judaism. Suppose the vegetarian’s ideals were universalized among all Jews. Where would the leather for tefillin come from? Not to mention the parchment for everything from mezzuzzot to Torah scrolls. Where would you get a shofar from? And I won’t even get into suede kippas or rabbit felt black hats. Would kaparot ever be the same? I'm sure non-Orthodox groups would adapt just fine, but what would happen to Orthodoxy?