The GamePigTM Entertainment Device from System Shock 2!
The MFD Game Player hooks up directly to any MFD, allowing the user to play games on their military grade cyber interface. A few cartridges may be found throughout the game, and the player can use their MFD to play those. However, the world continues on around them persistently, so the player can still be killed by varying elements of the environment.
In short you can play a GameBoy inside of the game and you can collect different cartridges throughout the main game itself to plug into your GamePig. In total there’s 6 cartridges you can find but if you use cheats you can get an additional 5.

The games are not big but there’s a lot more work put into these then you would think for something that has no impact at all on the story or the player.
Star Wars Knights of the Old Republic had Pazaak which was actually a fun card game and had some strategy to building a deck. I’m shocked Disney has not found a way to monetize this on mobile yet.
Voltorb Flip from Pokemon Heart Gold/Soul Silver is the best Pokemon mini game because it scratches the same itch as Sudoku/Picross. Please Gamefreak and Nintendo bring this to mobile I will pay you whatever you want!!
You can even play it online in a web browser.
I legitimately like Sonic Shuffle and think it is superior to Mario Party for reasons that are beyond this thread but this also includes the mini games!
The safe cracking mini game is a lot of fun because it relies on both players being able to work together really fast and if you are on the same wave length you can get a lot of them done.
Over the Rainbow is the mini game for me in this for some reason. It’s a really simple Simon Says knock off that gets progressively faster. The thing that is interesting though is there is no time limit. I have had 5+ minute long matches and it just gets really intense.