If you're looking for open-world RPGs similar to Skyrim or Oblivion where you can own a house without using real money, here are some options:
The Elder Scrolls IV: Oblivion
How to Obtain a House: In Oblivion, you can purchase houses in various cities by completing specific quests or achieving certain conditions. For example, you can buy a house in Anvil by completing the quest "The Siren's Song" or in Skingrad by completing "The Rosethorn Hall" quest.
The Elder Scrolls V: Skyrim
How to Obtain a House: In Skyrim, you can buy houses in several locations like Whiterun, Riften, and Solitude. Houses are typically purchased using in-game gold after completing specific quests or achieving certain conditions.
Fallout 4
How to Obtain a House: In Fallout 4, you can build and customize your own settlements, which serve as homes. This is done by completing the "Sanctuary" quest and then using resources to build structures.
Kingdoms of Amalur: Reckoning
How to Obtain a House: In Kingdoms of Amalur, you can own a house in the city of Rathir by purchasing it with in-game currency.
The Witcher 3: Wild Hunt (with Blood and Wine DLC)
How to Obtain a House: The Blood and Wine DLC allows you to own and customize a vineyard, which serves as a home base. You obtain it by completing specific quests in the DLC.
Minecraft
How to Obtain a House: In Minecraft, you can build your own house using resources you gather in the game world. There's no specific quest or condition; you simply need the materials.
Terraria
How to Obtain a House: Similar to Minecraft, in Terraria, you build your own home using resources found in the game. There are no specific quests required.
Kenshi
How to Obtain a House: Kenshi allows you to build bases from scratch. You gather resources and construct your own buildings, which can serve as homes.
Empyrion: Galactic Survival also allows base-building, but it's more focused on sci-fi survival.
Ultima Online and its custom shards offer home ownership, but it's an older game with a dedicated community.
FFXIV offers player housing in its MMO format, but it requires a subscription.
These games provide a mix of exploration, combat, and home ownership without requiring real money purchases for housing.