This question is somewhat of a tie in to my previous one "Should objectivists feel any sense of responsibility to their ancestors or descendants?" but is more specifically concerned with the rights of animals. If raping/murdering/cannibalizing etc. another human is a violation of their rights, does the same hold true for animals? Is bestiality acceptable to objectivists? Or, because animals are "lesser life forms" they do not deserve the same treatment? Is it wrong to treat animals without respect or dignity? Or is abuse acceptable?
While I agree with the answer by Javert, I don't believe it really gets to the heart of the matter, which is the nature of beings. Human nature is different from animal nature, which is why humans don't have the right to eat other humans (man's rights) but we can justify eating animals.
It's a pretty complex issue, covered in Objectivist literature, but consider some illustrative examples that may provide "food" for thought.
If you were walking in the jungle and a lion ate you, should the lion be prosecuted for violating a right? No, the lion is outside this context: man's rights and their protection through the political system he creates for his survival in a society of men.
If the lion eats a zebra, should the lion be prosecuted for violating a right? No, the zebra has no right (remember, a man made political concept) not to be eaten by the lion. The nature of animals requires that they survive by killing and eating other animals. Nature is tough.
Human nature however requires a different means of survival. We need to use our minds, and we need other humans to divide the labor required for survival as humans. Our nature is what justifies our right to be free to use our minds to survive (which included, once upon a time, the absolute need to eat animals to survive- whether this is required today is debatable. It is not a need nutritionally in America, but it may be in poorer 3rd world countries).
When we humans take an animal as a pet, and provide for its survival, then I believe that pet becomes our property, and is protected by our property rights, from other humans.
"Animal rights" is an invalid concept. Animals do not have rights.
The concept of rights relies on the concept of value. A right protects values (to humans) in a social context. In particular, expropriating the possessions of other humans (via force or fraud) does not create values; it destroys values. A right is the political instantiation of this moral fact.
However, expropriating the "possessions" of animals (their bodies, their labor, etc.) CAN create value; there is nothing immoral in using animals in this way (in fact, doing so IS moral, excluding edge cases such as bestiality, which does not provide value for the human engaging therein). In other words, there is no moral principle that would give us reason to grant rights to animals; rather, it is IMMORAL to grant rights to animals.
Hope this is helpful.
Further references: Ayn Rand Lexicon article on "rights" (can be found via Google); "The Objectivist Ethics" essay in "The Virtue of Selfishness"
answered Jan 26 '11 at 00:30