The OSR has several games where you can attempt anything that your character can do using mechanics that are simple to play and to setup yet have enough detail for many sessions of play.
Unlike computer games or board games these OSR games, like all tabletop roleplaying games, feature the ability for the player to attempt anything that their character can do within the setting. With their actions adjudicated by a human referee who uses the player's input, the rules and his adventure notes to make his ruling.
Most RPGs released by the OSR community revolve around the fantasy genre. They feature mechanics that have been played and supported since the release of the first roleplaying game in the mid 70s.
Most fantasy OSR games defines characters in terms of six attributes, a class defining that character's profession, and their equipment both mundane and magical. Characters are quickly generated with many folks ready in 15 to 30 minutes.
For the novice referee the most straight forward setup is to draw a small town with a few shops. Then just outside of the town in a out of the way place place a dungeon. The dungeon consists of a maze with rooms. The rooms are either occupied by monsters, have traps, have treasures, something unusual, or any combination of the proceeding. It is recommended that you have a few empty rooms or long passageway to spread out the occupied areas.
A dungeon can be setup "realistically" with various rooms occupied logically by those who inhabit that area. It could be setup as funhouse where anything and everything can be found in the various rooms. Often justified as the work of a mad archmage or wizard. Or any combination between.
Dungeons are organized into levels where the deeper you go the more difficult the creatures, and traps are. But the treasure is also correspondingly more rewarding. Within each levels you can have areas of related inhabitants. You can also setup these areas as competing factions for the players to learn about and take advantage of.
The prime role of the players during the game is to act as if their character sare really there. To listen to your description, respond to your NPCs, and act accordingly. Some players will act out a different personae while other will essentially be "themselves". Either method or anything between will work the only requirement is to interact with the setting you created as if they are there.
The various fantasy games produced by OSR support this mode of play very well due to the legacy of the mechanics they inherited from the first roleplaying game ever made. However the dungeon is not the only type of adventure possible with these game. The mechanics are flexible enough to support just about any type of adventure you can imagine those character are capable of doing.
There is a wealth of supplements and adventures to draw on for when your time or imagination is in short supply. Also many of these products expand the type of possible characters and give further support to specific types of adventures.
Many of these products are free both in terms of cost and creativity. Much of the OSR is bluit on the ideals of open gaming where the only thing asked of folks using their materials is to in return share what they created under the same term. This is regardless whether the work is just for fun, non-commercial, or commercial.