My style of play has been strictly solo play for the better part of 10 years. As such, my player and I have swapped roles as DM. It is a much more focused forum for decent storytelling and many of our stories have been more focused on NPC interaction than rote adventuring.
I have often played 2 characters side by side with a supporting cast of 2-3 "core" NPCs controlled by the DM. This has resulted in lots of hilarity as I often have played the characters as a 'team' with clearly defined and differing (often conflicting) personalities.
Example: younger brother, 16 yrs old - human fighter/rogue - your typical plucky, overeager hero who believes that brute force can solve most problems and proves it on a daily basis; older sister, 21 yrs old - human Favored Soul of (our campaign's Light goddess) - former barmaid, responsible, well-mannered and well-spoken, has a sense of humour reserved for her female friends as the men in her life have proven to be idiots, including her brother.
Example: Drow (in our campaign, Drow is just another non-evil subspecies of Elf) Priest of Knowledge - sarcastic, dry wit, sees humans as children, treats them as such; Human Ranger (Detective aspirant); speaks slowly and controlled, tries to solve issues using brains over brawn but has the brawn when necessary, prefers to handle situations with minimal bloodshed.
When I DM a solo campaign, the player IS the campaign. Everything revolves around the player, and while other things can happen, those things are always related to the player in some way. Sandbox is generally how I DM, and most ideas for adventure come off the hip as I go.