When DMing for one person, I do take a pretty different approach. There's no worry of keeping loot balanced for the entire party, it's alot easier to tailor the story specifically to the single player, and perhaps use (or abuse) elements of their background. It's very easy to bring up repercussions for their previous actions because you don't have to be wrried about disturbing the entire party cause one person lets their rogueish tendencies get the better of them. It is alot more personal, but, it can lead to some more involved stories then trying to sandbox play a party of five in my experience.
When I run a personal game, it's heavily dependant on who the player is. In most cases, I can only find time to roleplay with one particular friend and he's not the best with puzzles or hints, so, in tailoring games for him, I look to videogames for plotlines, things he'll sink his teeth into right away. For other friends, I try to make them investigate more, learn more about the world I have envisioned for them to explore. Since it's only a single player, it works alot like Oblivion or other RPGs where tey can create whatever story they want in the long run.