Quest

A quest gives a game structure without needing a story. There's an objective, there's distance between you and it, and everything in between is the game.

Subby Quest is the most traditional of the three, built around working through obstacles toward a goal. Cup Quest keeps things lighter and shorter, so it suits a quick session rather than an evening. Brawl Hero approaches the same idea from the combat side, where the objective is reached by getting through whatever's standing in front of it rather than by solving anything. None of them ask for much commitment before they get going, so you'll know within a minute whether it's for you.

There are 3 free games under this tag, all playable in the browser with nothing to install, and none of them ask for much commitment before they get going.

The exploring end belongs with Adventure games, and Collecting Games covers the fetch-and-gather side of a quest.