Streamlined games with straightforward controls & mechanics for short, casual playing sessions.
Casual traditional platform jumper games, where the player has to get through stages by jumping, running, gliding etc. while avoiding obstacles and/or enemies.
Example games: Subway Surfers, Super Mario Run, Jetpack Joyride
Games with a so called "idler" mechanics, meaning the game plays itself even if the application is closed. Additionally, when the application is open, players can see that progression is made all the time - even if they're not doing anything themselves (e.g. money keeps generating).
Example games: AdVenture Capitalist, Idle Miner Tycoon, Tap Titans 2
Lightweight extremely simple casual games that rely on straightforward controls and one-dimensional core mechanics. These games are figured out in an instant which is part of their appeal.
Example games: Helix Jump, Knock Balls, Snake VS. Colors
SHOOT 'EM UP
Arcade style, shooting games with simple controls and a LOT of shooting with no real emphasis on precise aiming or tactics/strategy.
Galaxy Attack: Alien Shooter
Example games: Galaxy Attack: Alien Shooter
Arcade games that don't really fit in any other Arcade sub-genre but are casual games with clear arcade nature and mechanics. Games like Bowmasters, Agar.io, Pirate Kings and Tank Stars belong under this sub-genre.