I've run solo campaigns in person from time to time, but it has always been a side adventure connected to a larger campaign.
It is certainly possible to run a solo only adventure, but perhaps more challenging, as the Dungeon Master becomes the only source of character interaction the player gets.
JB used to have many solo Role-playing Games here but since he stop running FE and World of Medieval I do n't see them anymore. They were a good way to build up character experience before joining a higher level party.
This works out alright until the player has to leave and the game is lost. At least when you have more than one player the game can still continue.
I believe this can happen once they focus on the game and not what they are missing. Some of the best game moments comes with two players because there isn't as much distraction.