This is the September/October 2011 LD resolution. I can see many arguments to be made for the affirmative and a few arguments for the negative, which I will outline here. Assume that “animal” refers to “non-human animal”, because defining “animal” ambiguously would lead to serious arguments over semantics.
I will begin by talking about my favorite system of ethics, Utilitarianism. Under this system, it is clear that failing to recognize the importance of animals is to miss out on a huge source of happiness and suffering. Any ethical theory that grants rights to beings capable of suffering must acknowledge non-human animals.
Some ethical theories only give moral worth to beings capable of reason. Some animals, such as chimpanzees and dolphins, are capable of self-awareness in the same way that we are and are in some sense capable of reason. But this is not always enough: consider Kant’s formulation of the categorical imperative. He wrote that “every rational being must so act as if he were through his maxim always a legislating member in the universal kingdom of ends.” In effect, for an animal to have moral worth it must be capable of comprehending the maxims of ethics, which I do not think a chimpanzee or dolphin is capable of doing. Therefore, according to Kant, animals do not have rights.
Whether animals deserve rights depends on how rights are derived. If the capacity to suffer is the source of rights, many species of animal would be granted rights. If rights instead stem from self-awareness, only a few animals would have rights.
There are very few properties that humans have that no other animals have, so it would be difficult to make an argument against animal rights without resorting to speciesism. The only way I can see to do it is to argue that rights in some way stem from the capacity for sophisticated abstract thought, e.g. Kant or contractualism. Contractualism, the belief that rights stem from an implicit contract made between the members of society, does not necessarily grant rights to animals since even the smartest animals are probably unable to comprehend the concept of the social contract.
Returning to Utilitarianism, it may be possible for the negative to argue that exploitation of animals increases utility overall. However, making such an argument would require assuming that humans are capable of far more happiness than animals, which is almost certainly not true and should be pretty easy to refute.
For a more thorough review of this resolution, see Decorabilia.