I've played many a session with just a single player; very often a prelude to the adventuring party meeting up, setting the back story and giving each player a unique start to the adventure. Sometimes a solo quest may poke its head above the parapet that deserves to be explored further — even if you're in a group taking time out to run a single player session can have its advantages: the whole group isn't kept waiting with much twiddling of thumbs; the story may be furthered by the rest of the party not knowing what is going on or maybe the player has missed a couple if sessions and their character needs to catch up with the rest of the group as they travelled through the silent forest.
That's not to say that you can't run a whole adventure or campaign with just a single player. If you only have one friend interested in gaming, then I don't think it shouldn't put you off playing at all, the experience will be very different to playing an adventure with six players, but nonetheless you can still have a lot of shared fun.
Before embarking on a new adventure though, be prepared that quite a bit more investment of effort is required by both the Game Master and the player — they'll be in the action continuously and won't have the support of other players ideas and skill rolls. There won't be any idle around the table moments where you can gather your thoughts, and especially with combat everything runs at a much faster pace. If you're using a commercial scenario then it's likely that the Game Master will have to scale back the encounters appropriately, this will take some time and you may need to get creative to balance things out — experience will help, so don't worry about making changes on the fly if need be. You'll have to look at the skills needed as well as balancing encounters, does the character have the skills needed to overcome the many challenges that can be contained within a given scenario? If the character is a fighter for example, will they be able to pick the lock of the vital chest? Maybe not so easily, but there should be a way around the problem with a little creating thinking.
There can be a huge amount of fun to be had crafting adventures and playing these small player count games. I've been blessed with some super sessions, one of the most memorable was a prelude to a campaign where I played a rogue in a Pathfinder session — entering the city with a mission to steal a gem from a powerful noble family — much entertainment was had planning the robbery; staking out the grand manor; carrying out the heist under the moonless night; before being chased by their guards over, under and between the rooftops and finally ducking down a narrow alleyway to safety. All the player characters had a similar single player session pre-campaign that set out how everyone came to know each other, our paths crossed and intertwined and our reason for adventuring together.
The vast majority of my gaming years were spent roleplaying with a Game Master and two players. There weren't really any clubs for us to join and none of our other friends were interested in this new type of gaming experience way back in the hazy dreamland of 1981, so our small group was all we could muster for our adventures in Gary Gygax's Advance Dungeons & Dragons (AD&D) Greyhawk setting or Marc Miller's Traveller.
However, we weren't put off roleplaying at all and neither should you be. Subsequently I've played in lots of campaigns with two players, and they've been amazing experiences without exception. On balance it's an easier game to run than with just one player, the Game Master isn't quite so pressured with the pace, two characters leads to more roleplaying opportunities player-to-player. Both players get a good amount of table time and there's rarely a lot of downtime either. For me I've found that having one Game Master and two players is the sweet spot for pacing, others may well disagree of course and I've had plenty of great four player games (I've struggled a bit with more than four though, for me there's too much down time and combat, particularly for the most popular fantasy systems can slow down to a bit of a crawl).
You will find that you will be lacking certain skills in your party, not so challenging as the single player game, but a challenge to overcome nonetheless. As players you'll have to use your whits to overcome obstacles that could have been solved with an adept skill role. If you're playing a fantasy roleplaying game with traditional classes then you may be struggling with life without a cleric with her healing spells and undead turning, or missing a ranger while traversing those distant misty marshes tracking a band of marauding bandits. Still, there's always a glass vial or two of healing potions — just make sure you don't land on them when you fall down that inevitable ten foot pit with a dusty looking skeleton lurking suspiciously at its bottom — or maybe you'll find a need to purchase a map of the marshes from a travelling salesman and his handcart of expensive curiosities from foreign parts.
Again, if you're running many commercial scenarios there may be some work involved in scaling back the encounters from their often expected four or six player counts. It may just be a case of reducing hit points of those treacherous bandits, or lowering their numbers to keep the marauders from overrunning your small party.
I'd highly recommend trying a session or two with a pair of players if you have the opportunity, I've found it to be absolutely fantastic over the years, and particularly for some types of games where there isn't the traditional classes like in Dungeons & Dragons or Pathfinder — some of my favourites going back over the (many!) years have been Vampire the Masquerade, Call of Cthulhu, Cyberpunk 2020, Legend of the Five Rings all of which have offered sterling one Game Master and two player storytelling experiences.
I have played campaigns where we each played a couple of characters to bolster the party numbers, and some where the Game Master payed a pseudo player character as well (not quite a non-player character, but playing as he would have a regular character).
For me though, I don't think it's something that I'd do again. I've personally found it to be more enjoyable concentrating all my effort on a single character — I spend a lot of time on my character's background and back story and find that two characters are too challenging in this regard. However, if it's something that you think would benefit your small group, then definitely give it a go — it could be right for you and be just what you're looking for. It does save a lot of time restructuring commercial adventures as the additional characters means that the Game Master doesn't need to tweak encounters to fit a small group. You will also be able to fill holes in the party with any skills that you may need; no longer will you have to rely on delicate glass vials filled with healing potions or a dodgy map of the marshes from a travelling salesman.
It's also a challenge to play different characters who know various things, some of which the whole party may not be privy to. It can be done, but it does require a bit of extra effort on the players to 'forget' what they don't know.
For me this has worked out better than running two characters per player; the Game Master takes control of them during the adventure which means that they have their own personality, goals, wants and needs. The player characters can talk to the party NPCs as they would a standard NPC; giving orders in the heat of battle; sending them on a side quest to discuss the local situation the priest while the main characters of the story head off to the palace for an audience with the queen.
Of course, depending on the nature of the NPCs whether they do as you ask or stir up more trouble for the party is up to the Game Master — this adds another dimension to their character and makes them all the more believable as a supporting cast of characters.
You can even swap them in and out as the adventure unfolds, maybe their sudden disappearance will be the cause of a new adventure? Or if the party needs specific skills for the mission ahead a new NPC can fill the role, will they betray the plucky group at the scenario's climax? Well that's another story.
Think of them as the cast of characters supporting the heroes in a novel or series, not minor NPC's but still major players in the story.