As a high school literature assignment, I was put on a team and asked to write a group paper about the intelligence of animals. We had to have an argument that they were, but also an argument that they were not. The other three members of the team strongly wanted to argue that they were, leaving me to write the argument that they were not. I mostly accomplished this by discussing some of the least intelligent animals, the ones that barely have a nervous system. But now that I've graduated, I'd like to discuss the topic in more detail. (The paper, like most of my other academic works, has largely been lost to the ages.)
First, I'm going to have to define terms. Humans are animals, and at least some are intelligent, but usually when this question is asked, it is referring to non-human animals, so I will work with this restriction. Intelligence is also poorly defined when this comes up. Let us define intelligence as the ability to comprehend abstractions, and adapt behavior to better prosper in the environment. This is slightly different from "the ability to score high on an IQ test," but there's enough overlap for our purposes.
Animals have a deep range of intelligence levels. On the lowest rungs are largely invertebrate animals that barely have a nervous system, and react to their environment primarily with a very limited number of pre-programmed instincts. Jellyfish and lobsters are good examples of this. For all their otherwise complexity, lobsters have about 4 responses to any stimulus. Hide from it, eat it, pee on it, and during the mating season, hurl gametes at it. Lobsters exposed to each other usually pick the "eat it" option, and are cannibalistic, much to the frustration of would-be lobster farmers. This is why lobsters in tanks have restraints (like rubber bands) put on their claws.
On the high end are some forest animals, often in the psittacine or primate families, who develop extremely complex, even cultural, behavior. They must learn from others in their social group, around an ever shifting environment, if they want to survive. They also need to fit cooperative social roles, as a lone parrot or ape is a dead parrot or ape. They are born helpless, and require rearing by parents, unlike the lobsters or jellyfish who are born self-sufficient. The record holders in this regard would be African Greys for the parrot group, and Chimpanzees and Bonobos in the apes, with strong progress shown by Gorillas. All four species have a noted habit of tool use, attempts at communication, complex social behavior, and very strangely enough, all are native to Africa.
I should also put in a bit about Dolphins. Dolphins have a complex society, and show many signs of intelligence. They have no tool-using ability due to their limb configuration, and live in a very different environment than us humans, which does frustrate communication attempts. Nonetheless, complex ideas have been conveyed to them and sometimes even understood.
Now, limitations. When testing the intelligence of animals, one must be on guard against cueing. Most of these animals are social animals that take cues from each other. When one finds food, it indicates to the others so that they can all share it, for instance. In the 1800s, there was a horse, "clever Hans," said to know mathematics. Later testing revealed the horse was actually taking cues from its owner, and didn't really understand mathematics at all. (It would indicate numbers by stomping its hoof, and later testing showed that Hans would just stomp his hoof until his owner nodded in agreement.) Similarly, a lot of parrots learn by imitation, as their social behavior does often involve mimicking each other's noises. Parrots will say a lot of words that they are unaware have any meaning, and owners of pet parrots often report that theirs will copy noises from the television, the telephone, ambient video games, the doorbell, and so on. Why? Because it's there. A parrot that has learned to say "Hello" or "I love you" may only think of this as a "human noise" to be imitated in the presence of humans. Similarly, the "signing apes" that have been taught sign language do spend quite a lot of time ignoring questions posed by their handlers in favor of pestering them for toys and candy, which speaks badly about their understanding of the language they're using.
Psychologists report on communication and language that some signs of intelligence in language use are re-combining words in novel contexts not spoken to them, "kenning" new ideas from old ones (such as Alex's description of an apple as a "banerry," from his known fruits of "Banana" and "cherry"), lying (which shows that one understands that other people do not have the same ideas that you do, an idea that human children do not understand until they are 2 or 3), and context appropriate grammar (respond to a "you" question with "I", instead of repeating "you.") Alex and his immediate successor Griffin may show these signs, but the average pet African Grey does not.
And after saying all of these facts, even the smartest non-human animal is rather dumb compared with an average human. Alex lived to be age 31, but his most advanced skill was one achieved by human child at about age 12, the ability to identify material composition. ("What matter, alex?") He was on average as intelligent as a 6 year old child, which in an IQ test would give him an IQ of 20. For comparison, IQ tests are weighted so that the human average is 100, and the standard deviation is 15 points, putting Alex, an exceptional parrot, as our most stupid of human beings, the ones barely able to talk and needing caretakers to change diapers and wipe away the drool. (An IQ of 20 qualifies a person as "cretinous," the lowest category.) Lobsters would be lucky to make a single IQ point at all if tested.
So, why the immense difference? Humans have specialized in being intelligent over the traits that animals use. Humans are very weak for our size, slow, more easily tire, are more easily damaged or sickened, and unlike the average animal, run the risk of choking every time we swallow. An animal the same size as a human is an immense physical threat if encountered without tools or weapons. Our only physical advantage is our heat distribution, which allows us to run immense distances without having to lay down and swelter for an hour after every mile.
But even at the beginning of human techology, this proved an overwhelming advantage. Early humans would construct elaborate traps and herd animals straight into them. With curiosity came experimentation, which lead to more technology, which has only exponentially increased our power.
So are animals intelligent? Not very. Some of them are slightly intelligent. Most are stupid in ways we humans can barely imagine.