2 Player Tabletop RPGs?

My suggestion is to use your favorite RPG, but make special scenarios for one player character. Standard scenarios expect the heroes to have four or five characters available, you'll have to downgrade the opposition significantly to give one PC a chance. Try to knock down the numbers of enemies to about a sixth of what the normal scenarios recommend, or substitute weaker monsters - goblins instead of hobgoblins, that kind of thing.

One-on-one always makes problems. Usually the best way is tailoring the adventure to the specific character - no one person dungeon-crawl. Systems that work one-on-one: Shadowrun, GURPS, maybe Call of Cthulhu and then there is always Wushu.

The first thing that you have to do when running a game for one player is throw out the challenge rating system that they set up in the books. Every situation is going to be tougher for one character. Then you have to design your own adventures based on the character type being used. The group mob mentality of playing goes away and you are left with a character that is always on their toes, excited at every challenge. Mission are more personal this way, and allow for more creativity and expression of the character being played. Essentially they become the most important figure in the story and they know it. Originally D & D was designed for about 5 player Characters to match blows with monsters. So they created a bunch of them and grabbed them from all the cultural sources they could find. This approach doesn't work as well with only character. Either the monsters are way too tough or they aren't a real challenge. So you have to make the monster secondary as major villains until you learn how to gauge this, and have goals that reward good role playing and problem solving. Missions like this include gaining information about what wizard X is planning next and when is the kingdom next door going to march. It means seeking personal items of interest and convincing others to help in the quest. It can mean family concerns are made primary. The sister got kidnapped by the thugs/bandits from X. Which is really only the tip of the iceberg of the story. But if you don't have a thief PC keep the number of traps either real obvious or low in number, and if you don't have a healer handy keep the combat down. Instead award points on accomplishing tasks and goals, and making good choices. The truth is that lots of TV and movies are set up this way. How many police dramas focus on one or two people? Conan is a single warrior making his way through the world. Superman confronts dangers while trying to be a normal person. They may have a minor sidekick (NPC) who helps with certain tasks, but leave the choice making up the player. If you do this, then your girlfriend will truly enjoy the game and will keep on playing it with you. Then as you have friends who can play for an evening occasionally then give them a character and have fun. So basically make it less about combat and more about story and you will have flipped the game to your needs.

I agree with Forvik, you have to change how the game works, make it less like D&D and more like a Choose Your Own Adventure sort of thing, more about investigating and adventuring than just straight up fighting. It would be really hard for a low level character to fight the kind of monsters that are in a D&D or D20 Modern campaign so it becomes more of a true Story Telling experience for both of the players involved. I like D&D with 2 players because it's more of a chance to explore the characters that your'e creating and to see what is happening in the world of the story.