Are animals under the curse?

Apparently creation has been given for man to tame, just as a horse would have been given to a bronco buster to break:

Genesis 1:28 NET God blessed them and said to them, “Be fruitful and multiply! Fill the earth and subdue it! Rule over the fish of the sea and the birds of the air and every creature that moves on the ground.”

Looking at the record, the bad attitude, the lying, blame shifting, disbelief and the actual disobedience, the subduing was to start with the serpent, the adversary, the bodily appetites within Man.

Quote from Article from Judaism.About.com

The Hebrew word "satan" literally means "adversary" and in Jewish thought one of the things we struggle against every day is the "evil inclination," also known as the yetzer hara. The yetzer hara is not a force or a being, but rather refers to mankind's innate capacity for doing evil in the world. Using the term satan to describe this impulse is not very common though. (The "good inclination" is called the yetzer hatov.)

Luke 4:1-4 NET Then Jesus, full of the Holy Spirit, returned from the Jordan River and was led by the Spirit in the wilderness, where for forty days he endured temptations from the devil. He ate nothing during those days, and when they were completed, he was famished. The devil said to him, “If you are the Son of God, command this stone to become bread.” Jesus answered him, “It is written, ‘Man does not live by bread alone.’”

Does it say in the Bible that the animals are under the curse of sin as well?

No.

Now, some groups may or not believe animals are under the curse, but there's no direct Biblical statement. Therefore, it would be a subjective, interpretation issue to address if they are truly under the curse or not.

Many YEC groups believe the curse affected not only animals, but plants, and even the universe itself via the law of entropy.

ICR, for example puts it like this:

The animals, not having moral natures, were not guilty of sin, of course, but they also shared in the Curse, for they were—like Adam—made of the dust of the ground that God had cursed. Like Adam's body, their bodies also must return to the ground. Henceforth, "death reigned ... even over them that had not sinned after the similitude of Adam's transgression" (Romans 5:14). Thus there is death in the world only because there is sin in the world. It is this great truth that causes evolutionists to stumble over God and His word. By stretching the six days of creation into great ages, many evolutionists can put up with the Genesis "story" of creation, but they simply cannot tolerate the record of man's Fall and God's Curse as the cause of suffering and death in the world.

But that's just ICR. They do not speak for Christianity as a whole, and I refuse to get sucked into a debate over whether their view is correct or not.

Paul does say that "the whole creation" (including animals, presumably) suffers because of the fall:

For the creation waits with eager longing for the revealing of the sons of God. For the creation was subjected to futility, not willingly, but because of him who subjected it, in hope that the creation itself will be set free from its bondage to corruption and obtain the freedom of the glory of the children of God. For we know that the whole creation has been groaning together in the pains of childbirth until now.—Romans 8:19-22 (ESV)

Francis of Assisi is famous for preaching to animals. Whether or not this is apocryphal, it illustrates his concern for non-human life. Wikipedia also notes:

Francis preached the teaching of the Catholic Church, that the world was created good and beautiful by God but suffers a need for redemption because of the primordial sin of man. He preached to man and beast the universal ability and duty of all creatures to praise God (a common theme in the Psalms) and the duty of men to protect and enjoy nature as both the stewards of God's creation and as creatures ourselves.

The final words of God in Jonah express compassion for both Nineveh and its cattle.

On the other hand, humanity is clearly distinct from the rest of creation:

Then God said, “Let us make man in our image, after our likeness. And let them have dominion over the fish of the sea and over the birds of the heavens and over the livestock and over all the earth and over every creeping thing that creeps on the earth.”

So God created man in his own image,
    in the image of God he created him;
    male and female he created them.

—Genesis 1:26-27 (ESV)

It would be a mistake equate the effects of sin on animals with their effect on humanity. It's also clear that creation will be relieved of its curse when we take on our rightful place as children of God.

Summary

The Bible, early Christians and many doctrinal frameworks assert creation has suffered as a result of original sin. But I don't know of any Christian group that puts the effects of the curse on animals at the same level as the curse upon humanity.