Here's some of the table top RPG games I love the most. Check them out!
My go-to game for pick up games, Fate Accelerated really focuses on story above everything else. It's rules-light, easy to pick up, easy to customize, and easy to run. For a short-run, story-focused game, you really cannot beat Fate Accelerated.
If you dig the narrative focus of Fate, but want just a touch more "crunch", Fate Core is a great option. It goes into more detail on using "aspects" as a game device. In many ways, the Fate system mirrors the way I think about games in general - it's like someone watched me thinking about stories and game me a system to define it.
Blades In The Dark is heavily focused on the fiction of the game experience. It includes some great systems for approaching mission-specific game play, managing factions and competing groups, and a great system for advancing "The Crew" of players as an almost independent character. It gives some of the best advice for running a game that I've ever read.
My favorite of the "Powered by the Apocalypse" games, it's another narrative focused game. It's unique in that it doesn't have GMs roll the dice at all - almost everything is player-facing. It also gives a great system for managing the threats and factions in a game world,
If you're looking for a bit more crunch, I've found that Ultramodern does guns and shooting and marries it to D&D, allowing you to do modern and future-based stories.
My current favorite for combat-intensive high-fantasy gaming, DnD does what it does, and does it well.