Mega Man (NES, 1987)

Level select screen, Replay beaten levels (to get the platform creation item, no e-tanks or tools like the balloon here)
Some ability gating (magnet beam for wily fortress, gutsman's block throwing ability to get the magnet beam (or elecman's beam but then you have to replay the level), freeze beam to freeze the fire pillars)
Gain abilities from bosses that are useful (but not required) against other bosses
Password save

Influenced by: Astro Boy (anime), probably SMB, Ghosts 'n Goblins, possibly Xain'd Sleena/Solar warrior, Alex Kidd, Castlevania

Influenced: Shubibinman/Shockman series, GG Shinobi 1-2, DuckTales 1-2, Krion Conquest, Cocoron, Bucky O'Hare, Ufouria, Alisia Dragoon, Darkwing Duck (NES/GB), Little Samson, Mistume ga Tooru, Pulseman, possibly Chakan, Battle Kid