In order for a game to be fun it must have three primary components. These three parts work together and if any one of them were to be removed there would be no game.Goals
A player must have an objective. This goal that the player is working towards needs to be clearly defined. There cannot be any ambiguity as to what the player should be doing or else they will feel lost. The objective to basketball is to get the ball in the hoop and score more points than the opponent.
This goal, however, does not need to remain the same throughout the game. One small simple starting goal could become a number of other goals later in the game. For example, the hero on an adventure might initially have the goal of delivering a package. Along the way a massive attack might take place leading the player on a quest to overthrow evil in his world. During this quest there could be many other smaller goals either independent from one another or building up upon each other to progress the story.
The point is, a player must know what he/she is expected to do at all times if possible. If the scope of the game is rather large then it might be best to break up the primary objective into a series of smaller goals. This will help give the player a sense of accomplishment along the way.
If there are no goals then the player will have nothing to work towards. The game will quickly become boring and the player will likely never return to it again.
Decisive Action
If a player has goals then he will also need a way to accomplish them. A player must be able to take the necessary actions to accomplish this goal. Going back to basketball, the actions allowing a player to get a ball into the hoop include dribbling, passing, and shooting.
In a video game there may be a number of possible actions a player might take, depending on what type of game it is. In an adventure game the player will be able to walk, slash a sword, and use items. In a racing game possible actions will include accelerating and steering.
If there are no actions for a player to take then it would not be a game -- it would be a video, story, or simulation. A game must be interactive. A player must be given the opportunity to manipulate the game's world.
Obstacles
The final piece to the game triad are obstacles preventing the player from accomplishing his/her objectives. These are challenges to overcome. In basketball, again, the obstacles come in the form of the opposing team. A player on the other team can steal the ball away before there is a chance to score a point.
These obstacles should not be impossible or even excessively difficult to overcome. If they are too challenging the player will become frustrated with the game and quit playing. However, the obstacles should not be too easy either. There must be a good balance in the difficulty. Progressively making the game more challenging the longer it is played will help span the skill levels of the player.
Another means of addressing the skills of the player are adaptive obstacles. In a video game statistics could be kept tracking the frequency of the player succeeding and failing at various tasks. These statistics could be used to modify the behaviors and characteristics of the obstacles to be either more or less challenging. For example, in an action game how frequently a player is hurt and how frequently he/she can regain energy could help determine how aggressive the enemies are going to be and how often health refills appear. Someone who is hurt often should have to face easier enemies and have more health refills so as not to become frustrated. A player who nearly never gets hurt should face more challenging enemies and be given fewer energy refills so as to not become board by how easy the game is.
Without obstacles it would not be a game. It would be idle activity at best and a chore at worst. There would be actions, but no challenge. If there was no challenge then the game would be rather dull.
Conclusion
As you see, these three parts all work together in a delicate balance to create fun. The games will the better balance between these three primary components will be more fun to play while those not so well balanced will be not worth playing.
I have played a number of games which are quite good -- along with a number which could have been better. If you are developing a game and it does not seem fun, assess those three elements. Maybe regaining some balance might involve removing part of the game you originally thought would be a good idea. Or, maybe, the fun could become better balanced by simply making a few tweaks here and there -- player speed, hit points, enemy behaviors, etc.
