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. One part is that when Cortex was talking to one of them, saying that a check has bounced, the penguins get angry. Cortex then asks if they want a fish, but they, via their voices, found out he drew his gun out and after one of them was shot, the rest of them leave in shock. They may have betrayed Cortex because of this (probably why they attack Crash and Cortex). They appear again chasing both Crash Bandicoot and Cortex on a snow ride shortly before Cortex's mother is heard. They didn't succeed in catching them so they exploded. 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.