I used to clean every level in Goldeneye and Duke Nukem 3D and then... just explore it or invent some story along the way.
For example, in Red Light District level of Duke Nukem 3D, I played as a demolition worker. First, I would go inspect the building in front of the strip bar, blow it to pieces, inspect the debris and finish my workday. Then, I would head into the 7-eleven, buy a magazine and head back to the strip bar for a well deserved rest.
In GTA3, I would work a week, as a truck driver, loading and unloading stuff from one part of Portland to the other and then I would snap and kill a lot of people before dying in a last stand.