Lots of games have minigames within them, but I've always found the shmup ones the most fun. It feels widespread enough that I felt like categorizing them.
I'm not sure if this warrants a concept page, but I wanted to make this list for at least my own reference.
Showing 1-10 of 10 items
Galaxian Perhaps the most famous example, its just the loading screen. When beaten, you unlock additional cars.
Galaga '88 Pretty similar to the previous Ridge Racer in that beating it unlocks more cars.
Space Harrier You can just walk into places and play Space Harrier.
Space Fever 2 Actually a sequel to a 1979 game from Nintendo. Its easily selected from the main screen, so while not hidden, it is an unexpected addition to a camera.
Pure White Giant Glastonbury Halfway through the game, Travis falls asleep on the subway and you play as Glastonbury, the mecha you see in his apartment.
Boxcelios A 3D shmup found in the SEGA Arcade.
Bizarre Jelly 5 You can play this anytime you are in Travis' apartment, and beating it unlocks a short animated video.
Ultimate All Shooters You can play as Ken, Ryu, or the Lost Planet robot.
Lost Viking You can play it whenever you walk into the cantina aboard your ship. The name is a reference to the Lost Vikings series, an older Blizzard IP.
Boxcelios 2 Same thing with Yakuza 3