Penguins in Crash Bandicoot 2: Cortex Strikes Back will generally walk left and right one time, spin, and repeat. These penguins can be defeated by a general side attack when they aren't spinning. They can also be jumped on at any time. Rarely, penguins will slide down hills facing the character, similar to seals in the forward-moving areas of the snow-themed levels.
In Crash Twinsanity, the penguins' movements reflect their personalities. When surfing on Cortex, penguins act as a background, never catching the player, but just filling in for the story. In Cortex's Icy Lab, however, when Crash walks close enough to a penguin, they will launch themselves at him in a straight line or into the air and blow up. In The Wrath of Cortex, the Penguins' form is much like the Crash 2 Penguins, appearing in the snow levels, but they waddle to one wall, turn around and spin to the other, and it will constantly do this until it is defeated.
Crash Bandicoot 2: Cortex Strikes Back
They are minor enemies in the snow/ice levels (Snow Go, Snow Biz and Cold Hard Crash). Here, they are one of three typical snow enemies, including porcupines and seals. Some penguins will walk back and forth, spin, get dizzy, and repeat the process. Others will slide down at Crash while walking forward.
Crash Bandicoot: The Wrath of Cortex
They appear in the levels: Arctic Antics, Eskimo Roll and Avalanche. They have the same role as the ones in Crash Bandicoot 2; walk back and forth, spin, and repeat the process. In the level Eskimo Roll, Crash can run over them with the atlasphere.
Crash Bandicoot Purple: Ripto's Rampage
They would have appeared as enemies in Arctic Cliffs, spinning and stopping like peguins did in the previous games.
Their largest role might be in Crash Twinsanity. In one cutscene, they confront Cortex about their pay, saying that a check had bounced. Cortex tries to calm them down by offering them a fish, but this only suceeds in making them angrier. Suddenly, the fish in Cortex's hand is replaced with his ray gun, which he uses to shoot the one he was talking to. This causes the other penguins to fly off in fear. They may have betrayed Cortex because of this (probably why they attack Crash and Cortex). They appear again chasing both Crash Bandicoot and Cortex during Slip Slide Icecapades. To defeat the penguins, Cortex can shoot them with his ray gun, or Crash can spin them. There are a lot of them in the Ice Climb level. They have jet packs that they can use to slide after Crash and Cortex (in the Humiliskate levels), charge at Crash, or fly in the air and try to dive-bomb Crash. These attacks are very easy to dodge.
They are also seen in Classroom Chaos inside some of the glass boxes along with other enemies.