Recently we switched gears from working on the more mechanically robust material for Sertorius to developing a rules light game called The Meddlers. We've made a lot of rules light games like Terror Network. We also made a game called Slayer published through Avalon Games that is quite rules light (highly recommend checking it out if you haven't). As a general rule, I think the lighter the game, the more fairness matters behind the screen.
Fairness is always important. A GM needs to have a sense of fairness in his or her judgment at the table. But when there are fewer rules, when the resolution system for each possible scenario isn't painstakingly charted out prior to play, then it matters even more.
Gamemasters are human, they are fallible and can't be fair 100% of the time. Fairness may even never truly be attainable in its purest sense, but that doesn't mean we should throw our hands up and say the only possible solution is for RPGs to have rules governing everything so there is no chance of the GM making a bad call. Fairness, like truth, is an ideal. It is something the GM should strive for. You cultivate it over it time by assessing your own biases and limitations, by examining things from the players' points of view and by serving the game, not your ego.
If you watch sports you know that some referees are more fair than others. None will make the perfect call 100% of the time, but there is a world of difference between the referee who makes 60% good calls and 95% good calls. Fairness can be learned.
I think the first step in becoming more fair as a GM is to assess your own biases. Do you reward the player who speaks the most eloquently over the player who stumbles over words, even when eloquence is not what is being judged? Do you use your powers to get what you want? Do you gloss over important details players mention, and fail to factor them adequately into your final decisions? Reflect on where you can improve and then do so.
One bias I think needs to be highlighted is when the GM favors outcomes that lead where he or she wants the adventure to go. At its worst this is railroading plain and simple. But there are grey areas as well. Sometimes you might not even realize you are doing it. When I know I am at a crucial moment, whether that is an NPC responding to a very important player question/request or deciding how the Grim Mage of Golhenna reacts to the player's net gambit, I ask myself internally whether my next move is being made to further my own agenda or to have the setting react as genuinely as possible to what is going on. Sometimes I find myself wanting things to go a particular way, so I remind myself that isn't the point, and put greater thought into my final decision. After a while, when you do this enough, you start caring about the outcomes less and less, and it becomes more intuitive (at least in my experience.
The Players Points of View
Examining things from the other side of the screen really helps me be more fair. This comes in two forms. The first is taking a break from GMing and being a player once in a while. The second is to just stop and think about who things look from their perspective.
If your a GM, chances are that is mostly what you do. I know some GMs who go back and between being a player and running a game, but most seem to live behind the screen. In some of my groups the GM position is rotational between campaigns, so this allows for me to dip in and out of either role.
When we designed Sertorius, I was a game master for the first half of its development, then I switched to being a player for the second half (with Bill as the GM). This was incredibly informative. It absolutely showed me flaws in my thinking about the design when I was only running Sertorius. To be a good judge, you have to know what it feels like to be on the receiving end of questionable judgements. So take a break from GMing and try just being a player every once now and then.
It's About the Game, Not About You
While there are always exceptions to any rule, I find the more a GM brags about his or her abilities behind the screen, the less awesome actual play with them tends to be. That isn't to say a GM shouldn't have confidence. I think confidence is very important, but when the game is just there to feed the GM's ego, that is a recipe for disaster because eventually players do things that will chip at that ego. I think to be a good and fair GM, you can't be too invested in the campaign/setting/adventure/etc as your creation and as a reflection of your capabilities. The more your ego rests on the campaign, the greater the danger here. A fair GM can accept constructive criticism and can also recognize when he or she has made a bad call or come up with a bad idea.
So serve the game. Work to make the overall experience, not your experience, as good as possible.