Does anyone know of any games that have arcade-style pick up and play but also feature some element of long form gameplay? This can be in the form of some narrative, a meta game or something in between.
The only example I can think of that I’ve played is Catherine, a puzzle-arcade game with a visual novel that bridges the game’s individual levels.
Indie games or retro games are both applicable.
As others have said, look into the Rogue-like genre. (And also Rogue, itself, if that’s your thing.)
I feel that Rogue Legacy and Rogue Legacy 2 deserve some mention here, for being essentially Mega-Man gameplay, but perfected.
In particular, Rogue Legacy 2 has difficulty sliders that can make it extremely arcade-like, such as maxing out both player and enemy damage, to make every encounter a one-hit kill.