There are many MMORPG virtual worlds out on many platforms. Most notable are IMVU for Windows, PlayStation Home for PlayStation 3, and Second Life for Windows. Many Virtual worlds have shut down since launch however. Notable shutdowns are The Sims Online and The Sims Bustin Out Online Weekend Mode.
Some single-player video games contain virtual worlds populated by non-player characters (NPC). Many of these allow players to save the current state of this world instance to allow stopping and restarting the virtual world at a later date. (This can be done with some multiplayer environments as well.)
Single-player games such as Minecraft allow players to optionally create their own world without other players, and then combine skills from the game to work together with other players and create bigger and more intricate environments. These environments can then be accessed by other players, if the server is available to other players then they may be able to modify parts of it, such as the structure of the environment.