In Surely You're Joking, Feynman recounts some great experiments he did on ants in his Princeton dorm room. See, e.g., here. My wife is totally uninterested when I do these types of things at home, but perhaps my kids will like it when they get a bit older :-)
...However, ants clearly are fundamentally different from us. A whimsical example concerns the work of ant morticians, which recognize ant corpses purely on the basis of the presence of a product of decomposition called oleic acid. When researchers daub live ants with the acid, they are promptly carried off to the ant cemetery by the undertakers, despite the fact that they are alive and kicking. Indeed, unless they clean themselves very thoroughly they are repeatedly dragged to the mortuary, despite showing every other sign of life.
The means that ants use to find their way in the world are fascinating. It has recently been found that ant explorers count their steps to determine where they are in relation to home. This remarkable ability was discovered by researchers who lengthened the legs of ants by attaching stilts to them. The stilt-walking ants, they observed, became lost on their way home to the nest at a distance proportionate to the length of their stilts.
The principal tools ants use, however, in guiding their movements and actions are potent chemical signals known as pheromones. ...
One can hardly help but admire the intelligence of the ant colony, yet theirs is an intelligence of a very particular kind. "Nothing in the brain of a worker ant represents a blueprint of the social order," Hölldobler and Wilson tell us, and there is no overseer or "brain caste" that carries such a master plan in its head. Instead, the ants have discovered how to create strength from weakness, by pooling their individually limited capacities into a collective decision-making system that bears an uncanny resemblance to our own democratic processes.
[How peculiar is it? Just replace the word "ant" by "cell" or "neuron" or something like that. Unless you don't believe in AI ;-)]
This capacity is perhaps most clearly illustrated when an ant colony finds reason to move. Many ants live in cavities in trees or rocks, and the size, temperature, humidity, and precise form and location of the chamber are all critically important to the success of the superorganism. Individual ants appear to size up the suitability of a new cavity using a rule of thumb called Buffon's needle algorithm. They do this by laying a pheromone trail across the cavity that is unique to that individual ant, then walking about the space for a given period of time. The more often they cross their own trail, the smaller the cavity is.
This yields only a rough measure of the cavity's size, for some ants using it may choose cavities that are too large, and others will choose cavities that are too small. The cavity deemed most suitable by the majority, however, is likely to be the best. The means employed by the ants to "count votes" for and against a new cavity is the essence of elegance and simplicity, for the cavity visited by the most ants has the strongest pheromone trail leading to it, and it is in following this trail that the superorganism makes its collective decision.