The more we look at the animals we share our lives with, the more signs of intelligence crop up. Take Moses the red-footed tortoise. When Anna Wilkinson, an animal cognition researcher at the University of Lincoln, in Britain, put Moses into a maze, the notorious plodder surprised everyone. He not only performed as well as any rat but also altered his navigation strategy when the situation changed - something beyond rats. Tortoises, it seems, are anything but slow.

But we humans tend to be most impressed by aptitude that resembles our own particular brand of intelligence. So which pets come closest to being our mental equals?

Chaser, a border collie belonging to American animal cognition researcher John Pilley, who has his own YouTube channel, learned the meaning of more than 1,000 words, including names for toys and instructions on what to do with them, such as "to ball, take Frisbee". Such feats required learning by inference, the same trick children use to learn language.

African grey parrots can do something similar but they go one better by mimicking our words. Alex, the African grey trained and studied by Irene Pepperberg, at Harvard University, in the United States, learned 100 words and even made up some of his own, including "ban-erry" - he already knew banana and cherry, and seemed to reason that an apple was somewhere between the two. Alex was also the first non-human to ask a question about himself, inquiring about his colour, which suggests an appreciable level of self-awareness.

When it comes to social learning, or looking to others for new information and skills, dogs are out in front. Whether or not this makes them brighter is a matter of opinion, however. In a recent study comparing the problem-solving abilities of wolves and dogs, the wolves figured things out 80 per cent of the time. Dogs succeeded only 5 per cent of the time and, more often than not, looked to a human to help them out. So it appears that for dogs, domestication may have encouraged intellectual laziness.

And while they are not commonly kept as companions, no discussion of animal intelligence would be complete without the corvids. Ravens, crows, magpies and their ilk are staggeringly smart: they solve complex problems, make and use tools, remember where they hid food and plan for the future. And that's exactly why they make for demanding pets, prone to messy habits like stashing prawns among the dishcloths.

Best for … caring

This is an easy one, right? Dogs care about their owners and cats don't. Actually, it's not quite that simple.

Last year, it emerged that, despite their aloof reputation, cats keep at least one eye on their owners' feelings. Psychologists Moriah Galvan and Jennifer Vonk, at Oakland University, in the US, found that cats were more likely to rub their owners' legs, purr at them and jump on their laps when the owner was smiling compared with when they were frowning. That's rather sweet. Then again, it suggests that, when you need some TLC, a cat is likely to give you a wide berth, which doesn't sound particularly empathetic.

It's fair to say dogs have more empathy. A recent study showed that dogs were more likely to approach for a snuggle when a person was crying than when they were talking or humming. And unlike cats, which watch only their owners, the dogs would go and check on a complete stranger if they sounded distressed.

Dogs are also the only species that have been reliably shown to "catch" yawns from humans. And like their owners, they are more likely to catch a yawn from someone they are close to than a random stranger. What's more, our canine companions have got our backs: a study out last year showed that dogs shun people who they see being mean to their owners.

On the other hand, one recent study revealed that your "best friend" doesn't love you back as much as you think. Researchers found no correlation between what owners reported about "emotional closeness" to their pup and the dog's behaviour in an experimental scenario designed to measure the extent of their attachment to their owners. Put simply, there was no evidence to back up the idea that because you have a strong emotional bond with your dog, it feels similarly close to you.

Several other pets, not least rats and mice, seem to get distressed when another of their kind is hurt. But there is no evidence to suggest that they give a flying fig about how we feel.

Best for … entertainment

Although dogs can be trained to do things that look like dancing, you won't catch Fido freestyling on the dance floor or tapping his paw to the beat. In fact, while the ability to spontaneously move to music is universal across human cultures, it is rare in non-human animals. Parrots, though, have definitely got some moves.

A sulphur-crested cockatoo called Snowball hit the headlines in 2009 when Aniruddh Patel, who studies music cognition at Tufts University, in the US, showed that it could rock to a beat. To see if the bird could adapt its dance speed to the beat, Patel played Everybody by the Backstreet Boys - one of Snowball's favourite tunes - at different speeds. Sure enough, the cockatoo was always able to keep time, bobbing his head, lifting his legs to the beat and squawking along in all the right places. Other species of parrots and budgerigars have been filmed doing something similar, apparently with no training.

Patel speculates that their grooving prowess might have much to do with their ability to learn sounds. Being able to mimic something you have heard requires a tight link between the sound-processing and movement-planning parts of the brain, he says. This might allow parrots to predict when the next beat will come and time their movements accordingly.

We don't know how many other species can dance. Initial studies have shown that sea lions can pick up a rhythm with training. So far, though, parrots are the only animals commonly kept as pets that can do it without instruction from their owners - and, it has to be said, with no little style.

Best for … the planet

When Brenda and Robert Vale published their book Time to Eat the Dog? The Real Guide to Sustainable Living, in 2009, they knew it would be controversial. They didn't anticipate receiving death threats.

Their calculations - that a medium-sized dog is as bad for the environment as a large SUV - make for difficult reading. It all comes down to the amount of land needed to grow their food. Dogs are out and cats are not much better, particularly given their penchant for bringing in dead birds.

The greenest pets are vegetarians that you later eat, the Vales say. So chickens, which produce a sulphate-rich manure as well as eggs, are strong contenders, as are goats, neither of which are that practical in Hong Kong, of course. You might consider instead guinea pigs, which are commonly eaten in Peru. If you can't stomach eating your pets, however, the goldfish is a good choice.

Robot pets could offer another green option. Sony's robotic dog, Aibo, was a commercial failure, but people did fall for it. When researchers compared how children responded to Aibos and real dogs, they found that children see the robot dogs as something in between: a piece of technology but one with mental states and social status.

It sounds daft, but it might explain why Japanese owners began giving Aibos funerals after Sony stopped supplying parts and updates in 2014.

Pet peeves

The received wisdom is that pets are good for our health - but the picture isn't quite that clear.

Studies have shown that having a dog in the room - assuming you're not scared of it - lowers heart rate and blood pressure more than being with a good friend or spouse. Just watching fish in a tank or stroking a pet, whether it's a cat or a boa constrictor, does something similar.

Explanations for the "pet effect" vary. One is that cute animals stimulate the release of a hormone called oxytocin, which can make us feel loved up, happy and calm. Another is that animals, including less cuddly ones, such as birds, fish and stick insects, give us the feeling of being connected to nature - something that has been shown to reduce stress. Yet another is that because pets can bring us together with like-minded people, they might foster social interaction.

But Harold Herzog, a psychologist at Western Carolina University, in the United States, is not convinced. He points out that there are as many studies showing that pets have no effect on blood pressure, and at least one showing that pet owners are more likely to get ill or depressed than non-owners. In one study, pet owners were more likely to die within a year of having a heart attack than people with no pets.

Then there are the parasites. Toxoplasma gondii, which makes rodents less fearful, can only reproduce in cats. Most of the two billion people thought to be infected with the parasite won't notice, but some will get a flu-like illness.

According to Herzog, then, if you are getting a pet for the health benefits alone, you might be barking up the wrong tree. 

New Scientist