It's quite remarkable but about 90% of the time when I mention I raise pigs, the response is "Oh wow, pigs are SO smart." I'm guessing that most of the folks who say this have no experience with pigs, but I even hear some farmers say this as well.
If "SO smart" means smarter than other animals, I respectfully disagree. To me, being smart means you have more ability to use your brain's cortex than would be expected. In other words, to think through things a little more. To anticipate. And REALLY smart would be to learn and anticipate the consequences of an action that occurs with regularity.
If you think that sounds like a fair definition of what it means to be smart, I submit the following examples of behavior I see every year from pigs who are free to express themselves.
- The pigs can pass from one pasture into another through an open gate and they do so daily. But if they see me doing something on the other side of the fence a little uphill from the gate, they approach the fence as though it will magically open to let them through. Then the group stands in bewilderment for a couple minutes trying to figure out how they're going to get to where I am. Finally one of them figures it out and dashes for the gate and most follow, but there are still one or two who just can't figure out why they can't cross through the fence and get quite frustrated when they see their herdmates suddenly appear where they want to be.
- Twice a day, I walk into the pasture and put their feed into several containers spread out over a small area in the pasture. I always make the circuit in the same order. Usually the pigs are lined up at the first container and they know the routing. But if the pigs show up after I've finished the feed bowl circuit, they all fight over whatever container they reached first. They don't think to check whether the other containers upstream or downstream already have feed.
- Some of the pigs routinely flip feed out of their container while they're eating, trampling it into the dirt or mud and never coming to the realization that this reduces their ration.
- The pigs have a mud wallow to stay cool and a large trough where they can sink into deeper water to cool off, but they'd rather try to step into their small drinking water trough and foul their drinking water or empty the whole trough by flipping it. Then they drink the muddy water in the wallow. I tried the nipple watering system with various incentives on the nipple (peanut butter, honey, etc.) but they could never learn to use it. Chickens do better.
Someone told me that pigs must be smart because they were trained to perform in the wild west shows. But other animals that are taught to perform tricks in shows include dogs, horses, lions, tigers, elephants, seals, and dolphins.
Don't get me wrong, I don't think pigs are stupid. I think they are perfectly adapted to survive in the way that they need and I love to observe them. But I don't think they smarter than any other domestic animal. If you've been around horses, cattle, sheep, goats, cats, dogs, birds, any of them can become really good at manipulating the situation to get what they want, which tends to be either food or freedom.
So where does the idea come from that makes most people believe that pigs are smart? I propose two sources.
- Pigs have a general reputation for being slovenly. You know, the mud wallowing, the smell, the rush to get at food, and all of the behaviors that have generated expressions such as "eat like a pig" or "this room is a pigsty." From this low reputation, we don't expect much in the way of intelligence, so it's a surprise to hear that they can make fine house pets. I hear people say "pigs are actually very clean" and I think that's a reaction to the same stereotype. If a pasture pig plants a nose on your pants leg, you'll find out how clean they aren't.
I believe that pigs are just as good as getting what they want as any other farm animal or pet. But not better. I'm thinking cows get a similar bad rap. (The Secret Life of Cows is a good read.) Observing any animal is fascinating, not to see whether they have intelligence, but rather to see how each species, and each animal within a species, manifests it. Pigs are amazing destroyers. Put anything in their pasture and they will find a way to ruin it. Exactly what you'd expect from an animal built to push. That doesn't make them smarter than other species. 
Pigs are herd animals in a big way. People tend to be familiar with the herd behaviors of horses, goats, and sheep, the predominant feature being galloping away in a mindless panic from anything that surprises them. I've seen pigs do that too, especially piglets. But pigs are quick to approach a novel object or sound out of curiosity, and as soon as one does, the others are right behind. That curiosity is often taken for intelligence, which might lead to the conclusion that they are smarter than sheep, goats, etc.
But keep in mind that even though pigs are herd animals, they are not prey animals, at least they aren't nearly as vulnerable as other herd animals. Mountain lions (called cougars locally) kill prey by a bite to the back of the neck and pigs don't have a very good neck for that. It's possible for a cougar to take a pig but not likely. And pigs are just too big for smaller predators. Thus the herd behavior that you see in pigs is not the same as that in herds of sheep, horses, and so on, where running away at full speed is often the smartest option.
Therefore, if you tell me how smart pigs are, my response will probably be to laugh. If you say it when I'm drinking something, I may snort it out of my nose. If you disagree and think you have a good argument, I'd love to hear from you.
Quotes and Trivia
Studying cows, pigs and chickens can help an actor develop his character. There are a lot of things I learned from animals. One was that they couldn’t hiss or boo me.”
– James Dean