From the Super Mario Wiki
Penguin Mario (Penguin Suit Mario in the original Prima Games guide) is a power-up that debuted in New Super Mario Bros. Wii. In general, the power-up enables the player to move faster by sliding on their belly.
Super Mario series
New Super Mario Bros. Wii
Mario becomes Penguin Mario after gathering a Penguin Suit. After Mario has become this form, he can throw Ice Balls at enemies and freeze them. Mario can then use the frozen enemies as platforms or pick them up and throw them against the wall or other enemies. He also gains a good traction on ice, stopping him from slipping like normal Mario. While in this form, Mario can slide on ice with great speed, defeating some enemies and destroying Brick Blocks, allowing him to find secret areas. If he gets a running start, Mario can also slide a considerable distance on the surface of water, and can jump up from the water in order to obtain certain Star Coins or blocks. Also, while in this form, Mario can be controlled underwater using only the direction pad, as Frog Mario can be in Super Mario Bros. 3.
New Super Mario Bros. U / New Super Luigi U / New Super Mario Bros. U Deluxe
Penguin Mario also appears in New Super Mario Bros. U and New Super Luigi U. The catch is that the suit can only be obtained in the Toad Houses in Superstar Road. Otherwise, it acts much the same as before. The suit is also used in a few Challenge Mode levels. In New Super Luigi U, however, the suit can be obtained within certain levels in the game, in spite of the fact that the Luigi levels are supposed to be based off of the penguin-free Mario ones.
Super Mario Maker series
In Super Mario Maker, Super Mario Maker for Nintendo 3DS and Super Mario Maker 2, knocking on a door in the New Super Mario Bros. U and Super Mario 3D World styles will occasionally cause Weird Mario wearing a Penguin Suit to peek out.
Mario & Sonic at the London 2012 Olympic Games
In Mario & Sonic at the London 2012 Olympic Games, although Penguin Mario does not appear in the game, there is a suit based on him that the player can unlock for Miis to wear. It is one of the suits unlocked after paying 10 blank cards. The same suit also appears in Mario & Sonic at the Sochi 2014 Olympic Winter Games.
Super Smash Bros. for Wii U
Puzzle & Dragons: Super Mario Bros. Edition
Penguin Mario also makes an appearance in Puzzle & Dragons: Super Mario Bros. Edition with Water and Fire elements. He has above average HP and RCV rating with average attack. Penguin Mario's skill, Dive, changes Light Orbs into Water Orbs while his helper, leader, or awoken skill is Ice Dance, which doubles any Water team member's RCV rating.
Mario Sports Superstars
Penguin Toads appear as selectable teammates in Mario Sports Superstars, with both yellow and blue varieties. They are classified as speed characters. Both colors are available in baseball, while only Blue Penguin Toads can be chosen in soccer.
Mario Kart Tour
Super Smash Bros. for Wii U trophy
Mario Kart Tour
Names in other languages