First, I should warn that I'm not a vegetarian nor do I play one on TV. My wife is one however, and there are many different reasons people make this choice: ranging from not liking the taste of meat, health reasons, moral concerns (which could include religious reasons) about animal consumption or the treatment of animals who are later consumed, religious beliefs about animals (think cows in "Hinduism").
Most of those who believe it is wrong to eat animals for philosophical moral reasons are types of consequentialists who think it is wrong to inflict pain and suffering on animals, because wrong is the infliction of pain and suffering, and animal suffering is identical or sufficiently similar in kind to human suffering (this is the argument put forth by Peter Singer).
You could also come up with a conclusion that it is in practice wrong to eat meat due to the treatment of animals who are consumed for meat that is not universally opposed to eating meat. Here, a potential Kantian angle is that Kant thinks enjoying animal suffering is immoral because it encourages us to enjoy human suffering.
A separate route is the similarity route which argues that insofar as it is immoral to kill humans, it follows that it is immoral to kill something that differs from humans in only the most minute regard -- since whatever the basis is for killing humans being wrong, it's difficult to grasp how a minute change would completely eviscerate that. (This is a type of argument by analogy). This route could be rejected if you think rationality is the definition of why human life has worth but not price.
A further distinct avenue is to accept the Kantian premise that what makes our lives have worth is that we are rational -- and to show that many animals (say Dolphins) demonstrate a degree of rationality that means we should afford them this protection. This is the logic behind say the PETA lawsuit arguing that Seaworld is slavery because whales are people. It seems that Kant would accept such an argument since our rationality and humanity for him refers not to our participation in the human biological species but insofar as we are rational creatures (thus, an alien on Kant's view would have humanity if it has rationality and empirical desires).
There's a separate thread somewhere on here about being vegetarian that might give you more to chew on.