I've run a number of successful D&D 3.5 / Pathfinder games for my wife using the Gestalt rules from Unearthed Arcana. Since she gets to pick two classes at full progression, she has access to a lot more resources than if she had one (unless she min/maxes one role - i.e. picking two classes for ultimate damage, which in this situation would be a pretty poor choice).
These games were both using published adventures (Rise of the Runelords) and adventures written by myself. I provide her with an NPC ally that's designed to fill a role her character is missing, and she directs what the NPC does. In our Rise of the Runelords game, I actually found I didn't need to modify the encounters much.
Long ago, I also ran a successful 4E game for her using the companion character rules I think from DMG2, and lots of minions. Worked well also.
I think the biggest problem to overcome is the lack of resources that one character has. If the character (and any NPCs) don't have the capability of disarming advanced traps or picking locks (for example), those challenges become much more difficult or potentially insurmountable depending on how the adventure is designed.