Why is Tetris so addictive?

Tetris gets the players into endless compulsive loops by providing them with a new uncompleted task the moment they complete one. As soon as you put a block to fill an empty space, the shape of your pile changes and you find that you need a new one to fix it again. This goes on forever.

Zeigarnik effect is a theory that says that uncompleted tasks have priority over everything and remain in your memory. Because Tetris keeps introducing uncompleted tasks (shapes that make the pile look out of order), a person stays hooked to the game.

We humans have the unconscious desire to maintain order and be in control. People enjoy piling Tetris blocks to get uniform shapes. People who have a stronger need to be in control than others are more likely to get more addicted to Tetris.

The fact that the shape that comes next isn't known makes the reward unpredictable. The brain gets bored when rewards are predictable, but with unpredictable ones hormones are released that improve the mood and cause addiction.

Because the game can never end, even if you finished all levels you will start again with a tougher setting, people can never get enough of it. People usually stop playing games when they win but if they can't win then they might keep playing forever. (See Why are endless running games so popular?)

The game appeals to males and females and young and old people. This helped it become even popular since it's not designed for any certain group of people.

Unlike most games which introduce unsolved problems that take a lot of time to be solved, Tetris frustrates the players by giving them unfinished tasks but allows them to finish them in seconds by placing the next shape. This prevents people from getting bored or losing hope. 

Tetris combines quick rewards with long term ones. A player can get one line removed fast or he can wait and remove 4 or 5 lines together. By combining both rewards the game appealed to a wider range of people.

Because Tetris is a fast paced game, a person has a very limited amount of time to think before he can act. This helps people become 100% focused on the game, forget about their problems and get rid of stress. (See Why Online Games are addictive?)