They are in many multicellular organisms. Some bacteria and yeast also have pigment molecules, but they are not inside specialised pigment cells, because they are unicellular organisms.
The most famous and important pigment cell is the melanocyte, that has a black/brown pigment called melanin. These cells are present in mammals (humans, mice, dogs…), and also in birds, reptiles , fish, frogs and octopus. The main function of melanin is protecting the rest of our cells from the UV radiation from the sun.
There are also other pigment cells, that have different pigment colours. We have a pigment cell that has a silvery pigment, and reflects light like a mirror. This cell is present in fish, reptiles, frogs and octopus. There’s another pigment cell with a yellow pigment, that is also present in fish, reptiles, frogs and octopus. Finally, there are also some pigment cells with red or blue pigment that, so far, have only been detected in fish.
As you can see there are lots of pigment cells with different colours to create the amazing pigment patters that we can see in the animals.