Understand your players
Your players are paying careful attention to you as they try to understand the game world around them. (See Players must understand your universe for more on this.) You should paying careful attention to your players to try and understand them.
Think about what you are teaching
Like children, players must learn how to interact with the world. While the game books usually tell you and your players about the world and society of the game, there remain huge grey areas that must be filled in by you. Your interpretations and preferences will take the general shape of the world and add the details that make it livable. Maybe a game says that a specific ruler is "mentally unbalanced and cruel." You'll need to decide, how crazy the ruler is, how cruel is he? Does he have any good sides? Is his sense of humor normal, or twisted and sick? Does he have a sense of humor at all?
The world of the game you run really only exists in your head. The players won't know what is acceptable and what is unacceptable until you teach them. Your players will see how your game world works and adjust their behavior to better conform. Expect your players to tend toward the path of safety and ease. As a result, you need to be aware of what you are presenting as safe and easy.
Typically the world of a role-playing game is full of strife, lies, and backstabbing. Evil often wins. All too often the players learn that their characters should become paranoid, harden their hearts, and only take sure bets. Not the stuff of heroes.
The most common example is NPC's breaking the PC's trust. Having a friend or ally to the players betray them is a fun plot element. It's a common theme in fiction, and it gives players an opportunity to wallow in a bit of angst. However, done too frequently, the players will decide that eventually most NPCs will backstab them and will stop trusting anyone. Now you can't do the plot line at all.
Two similar problems are "good always wins" and "evil always wins". If it seems like characters with unwavering faith never fail, the characters will lose their uncertainty and moral weaknesses. If the character willing to sell his soul always gets an edge, the characters will line up to start bargaining with the devil.
The answer is not to stop doing these plots, but to provide balance. Make sure that you show the benefits of behavior you want to encourage. Maybe one NPC betrayed the party, but look at the other NPCs who have been very helpful through thick and thin. Maybe Bob got supernatural powers for his dark pact, but as a result he is slowly losing his sanity.
Definitely make sure you are not repeating a message you don't want players to learn. Certain genres tend to reinforce certain lessons. Cyberpunk games tend to encourage greed and selfishness. Horror games tend to encourage paranoia.
A good example of the worst case is Scooby Doo. Every episode, the Scooby and gang stumbled across an apparently supernatural creature. Every episode the creature was revealed to be someone in a costume. This scenario repeated dozens of times, but they never learned. Probably too many "Scooby Snacks." Role-playing game players will learn after the second adventure and sucker punch the ghost five minutes into the third adventure. Scooby Doo is doomed to failure as a role-playing game.
FASA had problems with this in many of their early Shadowrun modules. There was a run of modules which all featured a plot twist in which the party's Shadowrun employer betrayed the party. These modules all taught that shadowrunning wasn't profitable, since your employer always reneged on the deal. Not such a good lesson for a game about shadowrunning.
Be particularly careful at the beginning of a campaign, or when adding new players to an existing campaign. During this time players are eager for lessons, trying to get a grasp on the world. They have no idea what sort of game you're planning on running and take their cue from you. These lessons will run deep, so strive to set the tone and lessons carefully.
Related is your attitude to the dice. If the GM decides to "let the dice fall where they may," players will become cautious, they'll avoid daring feats. If the GM rewards daring feats and fudges the dice, player's will take more and more risks.
Pay attention to your players
Presumably, you run your game with the intention of your players enjoying the game. It's easy to get focused on what you enjoy in a game, and miss what the players enjoy. Fortunately, it's as easy as paying attention to your players.
When your players are focusing on the game, you're probably doing something right. When your players are reading books, chatting about unrelated topics, or simply not showing up, you're probably doing something wrong.
You might even try simply asking what they've liked and disliked in your game.
Also pay attention to the lessons they've learned (see above). Sometimes players generalize patterns incorrectly ("Gee, the bad guy always gets away safely while we get battered. Maybe we should turn to lives of crime."). Sometimes players miss obvious patterns ("Gee, the last four men with spider tattoos on their hands have tried to kill us, but this one seems friendly enough.") Pay attention to how their characters are behaving. Listen to what players talk about and plan. If they're learning the wrong lessons, figure out why. Perhaps there is a pattern you didn't intend. Perhaps the cause and effect relationship wasn't obvious. Perhaps you are too close to your own plans and need to step back. You'll also need to see if you can take corrective action. Maybe breaking the pattern in a stunning way will do the job. Maybe you can simply tell the players out of character what's what.
PCs may chose death over defeat
Avoid making players pick between failure and the death of their characters. When something important to the characters is on the line the players may pick death, leaving you with the choice of making them roll up new characters, or inventing implausible ways for the characters to succeed.
Players are generally portraying heroes. Fictional heroes don't give up, even in the face of death. Fictional heroes usually succeed, in spite of the odds. These are the sources players will be following. (In some genres heroes strive in the face of death and die. In others the heroes aren't actually heroic and will worry about saving their own skin first. If that's the case make sure your player's understand it!)
I once began a Deadlands campaign with the destruction of the player character's home town. The razing had to happen, it was the key plot element for the next year of play. The forces arrayed against the characters were clearly overwhelming. The characters almost died in a battle to defend the town that they could not win. They were prepared to sacrifice their characters. They only survived because I approached them out of game and asked them to back down. Not a great way to get the campaign off to a start.
Similarly, avoid backing the characters into a corner. If the players feel trapped, they may gear up for a doomed last stand, blinding ignoring an escape route. If the players feel trapped but shouldn't, remind them of details they may have overlooked or forgotten.