There are two types of currencies that Crazy Cap uses: the regular gold Coin and the purple Regional Coins. These are exchanged in the purple or yellow sections of each and every Crazy Cap store. Each store sells a Power Moon for 100 Yellow Coins, which a reference to the Power Stars in Super Mario 64 and Super Mario Sunshine that revolved around collecting 100 Coins in the levels.
Similar to the Life Mushroom, this heart gives Mario twice as much Health as normal, allowing him to take up to six hits before succumbing to death, dropping 10 coins upon death. These hearts can also be found in the levels. If the player dies too many times in the room before the boss fight, a Crazy Cap salesman will sometimes appear to offer this item for purchase with nothing else.
Since the purpose of Coins in Super Mario Odyssey now replace a traditional lives system and can be collected ad infinitum from enemies that respawn frequently, Crazy Cap stores instead let you buy the Power Moon. This is opposed to the Power Moon showing up when you collect 100 coins in a level like it would be in previous games. When purchased, Mario will collect the Moon immediately after.
Every Crazy Cap store has several items of clothing to purchase that go into the closet of Mario's ship The Odyssey. These also pop up in closets in Crazy Cap stores. Costumes present no real advantages to wearing them aside from opening up doors guarded by a NPC that needs to see Mario in a specific costume before allowing him inside.
Crazy Cap stores also hold Souvenirs that can be purchased and are placed inside of The Odyssey. These all need to be purchased with Regional Coins. They serve no real purpose other than decorating the interior of The Odyssey.
Stickers are also purchasable in Crazy Cap stores, similar to Souvenirs in that they decorate The Odyssey. Unlike Souvenirs, Stickers only decorate the exterior of the Odyssey.
Crazy Cap appears to manufacture all the Brochures that appear throughout Super Mario Odyessey, as their logo appears on all the Kingdom's brochures regardless of whether or not they actually operate there (see Cloud Kingdom or Ruined Kingdom). This is a interesting note, as it would suggest they do copious amounts of research before setting down in a Kingdom and are part of a larger tourism industry in the Mario universe.
The Crazy Cap shop returns in Super Mario Rendezvous, with a very similar function. There is at least one in every kingdom or Neo Bowser City area, as well as one on the Koopa Subway. The Crazy Cap shop sells very much the same merchandise - outfits for both Mario and Peach, exclusive Power Crowns, and souvenirs - but they no longer sell stickers for the Odyssey. Instead, they sell posters to hang in your cabin on the Koopa Subway, as well as other decorations. Subway Tickets are also sold, which change what the interior of the train looks like.
The Crazy Cap shop makes its spin-off debut in Mario Kart Horizon, where it is accessible from the main menu. Stickers for your Karts and exclusive Kart parts can be purchased here using yellow Coins gathered on the track.