Player-DM-Trust
As a dungeon master, you almost can't avoid to "cheat" your players. Not just by changing a hidden die roll or the remaining hit points of an enemy, but by adapting the game world to the players actions.
Some examples:
1) In a big fight the players have had some bad luck with the dice and it's looking bleak. The DM has the monsters target the healthy fighter instead of the near dead wizard.
2) The characters must retrieve an artifact from the top chamber of a wizards tower but the dungeon master forgot about that Fly potion the party wizard still has. Because this would allow the players to bypass the entire dungeon the DM decides that all the tower windows are magically reinforced.
Both of these examples, I find bad. Because in either case, the players may feel, that the DM is "cheating". For the first example there might be more subtle ways to influence the fight. You could have an enemy caster not use the strongest spell in their repertoire. But sometimes you just have to let the wizard die. If the players get the feeling that you will intervene when they start to lose, that takes away the excitement of the game. Also it ruins the players sense of achievement when they win. This is why I dont make hidden rolls whenever possible (the only good reason to make hidden rolls in combat is so the players dont figure out your monsters attack boni and damage right away).
For the second example things get a little more complicated. Keeping the status quo would mean the players skip a large portion of your adventure. Maybe you didn't prepare anything else for today. Maybe something essential for the plot is supposed to happen inside that tower. Also, it will probably be more fun for everone to accept the challenges in the tower. As a DM, you should "cheat" in this situation. But you should carefully consider the way you do it. First, the change you make should be plausible and ideally the players shouldn't even notice. Second, using the Fly potion was a good idea and if possible it should not go entirely unrewarded. Maybe the wizard uses the potion to break into the top chamber and finds some cool loot, but the artifact the party was looking for is not there, because the owner moved it to another part of the tower. Never should a player be punished for a good idea, just because it breaks your plans.
To summarize: The players must trust you, not to make too many adaptions on the fly. To establish this trust it is necessary that sometimes things go really well for the players, and sometimes things go really bad. If you do not allow for these extreme outcomes, the players will feel like they have no influence on what happens.
Note: Some dungeon masters like to improvise most of their adventure and may do an amazing job at that. But if the game world is not pre-planned to a certain degree it is impossible to establish this player-DM-trust.
Use a Grid!
Just a few years ago, in my d&d party we used to run fights without a grid. Sometimes we used to sketch the scene and have the players mark the positions of their characters. Don't do this! Even if you run a game that does not have specific rules for movement on a grid, I strongly recommend making up some basic rules for that and using a grid and miniatures (or tokens) to keep track of positioning during fights.
It makes things more tactical, it allows you and your players to take advantage of the environment and it puts an end to those discussions about who was in range of that dragons breath and who was not.
More recently I have taken up running entire dungeons with a grid. I use big sheets of flip chart paper (which happens to have the exact size of squares for miniatures) and draw the outlines of the dungeon and sketch its most important features as the characters explore. Character movement is not turn-based during this. This once again eliminates discussions about who was in range of that trap and who was not. Also it allows for quick transitions into a fight. For some parts of the dungeon it may be tedious and unnecessary but if you run the entire dungeon with verbal description and suddenly take out the grid for one room, all your players will know that something is up. My players and I have been really enjoying this approach so far.
If you need tokens for monsters, I can recommend this, especially if you play d&d, but might work well with any medieval fantasy game.
Miniatures otherwise are kinda expensive. There are some less popular fantasy tabletop games like Mage Knight with good miniatures that are much cheaper in most stores. You might have to use a bigger grid though.
A Players Responsibility
(party from here: http://www.giantitp.com/articles/tll307KmEm4H9k6efFP.html)
All the players are just as much responsible to make the game good and enjoyable as the dungeon master is. This seems obvious. But sometimes players forget this, with the excuse that they are "playing their character". A player may decide that his character has no good motivation to pursue the quest the dungeon master presented. This is not good roleplaying! If the player insists on his character needing a good motivation, it is that players job to come up with a motivation.
Similiar, while some conflict between the player characters can be fun, it is ultimately the players responsibility to have their characters get along and team up for the adventure. This is not to say players should not roleplay their characters. It just means they should roleplay their characters in a way that makes the game fun for everybody.
Let Your Players Shine
When someone plays a roleplaying game, they want to be the awesome hero that defeats the bad guy and saves the day and there is no reason not to let them, at least from time to time. That means if your party rogue attemps a daring feat, swinging from the chandelier towards the bad guy, give him a fair chance with the dice, even if you think the move is a little unrealistic and he might just as well have taken the stairs. If the roll is successful, describe how the bad guy is astonished and takes a step back. When the party bard gives a performance at the tavern, let him notice how the young barmaid is staring at him and blushes and shyly turns away as he looks back. When the dwarven fighter lands a critical hit on the orc barbarian, describe how his mighty blow crushes the orcs skull. Also, do not have a super strong NPC turn the tide of the final battle and take the glory away from the player characters.
In other words: Let your players be heroes.
Other Example: A Player rolls a critical hit and the DM just tells him "you kill the guy" without the player rolling for damage. Even if the enemy only has 1 hit point left, let the player roll the damage and probably even give some description of the amazing blow the player landed.
Link to Part 1