No, I don't believe animals have any rights whatsoever nor do I believe they should. I believe that when God created us, He gave us dominion over all animals.
"God blessed them and said to them, "Be fruitful and increase in number; fill the earth and subdue it. Rule over the fish of the sea and the birds of the air and over every living creature that moves on the ground." Genesis 1:28
"Then God blessed Noah and his sons, saying to them, "Be fruitful and increase in number and fill the earth. The fear and dread of you will fall upon all the beasts of the earth and all the birds of the air, upon every creature that moves along the ground, and upon all the fish of the sea; they are given into your hands. Everything that lives and moves will be food for you. Just as I gave you the green plants, I now give you everything." Genesis 9:1-3
However, along with the dominion, we were given responsibility. I have no problem with eating meat, wearing leather (or even fur if I could afford it), medical testing, hunting, fishing, entertainment, etc. I have a problem with people who can torture an animal to death by putting it in a microwave, pouring gasoline on it and setting it on fire, starving it, etc. Most serial killers begin with cruelty to animals before moving on to bigger and better prey, so I'm all for those people being kept away from the rest of us. *nods a lot*
"If you see the donkey of someone who hates you fallen down under its load, do not leave it there; be sure you help him with it." Exodus 23:5
"A righteous man cares for the needs of his animal, but the kindest acts of the wicked are cruel." Proverbs 12:10