First and foremost, the game must be easy to start. From the opening menu (if there even is a menu) the player must be one click or tap away from the game. This low barrier to entry is easily seen in a slot machine. All you need to do is walk up, insert a coin, and pull the lever.
Next, addictive games have a simple, repeating feature. For a slot machine, you insert a coin and pull the lever. For Flappy Bird, you tap the screen to jump your bird higher. For oO, you tap the screen to switch from one side of a circle to the other. In Space is Key you hit the space bar to jump. Those descriptions areall you need to know about those games. That is it. Those are the mechanics. Simple, repeating actions that turn into an addictive experience. The simplicity of these mechanics do not necessarily make these games easy, but they do give the player motivation to keep going. Come on, how can I be losing? All I need to do is tap the screen at the right time! The simple mechanic gets into the player's head as the game difficulty increases. "The input is so simple, but the game is so hard," they think to themselves. This, in turn, causes them to double their focus on the game.
Much like a slot machine, this simple mechanic can be dressed up with catchy music, slick sound effects, and gorgeous visuals. These attributes are not necessary, but they do add to the experience by giving the senses a feast of input.
The final important attribute is to make the game easy to start over once you reach a fail state. In Space is Key and oO the player instantly respawns. In Flappy Bird you are three taps away from starting over. Imperceptible loading times are important to keep the player in a "just one more" state of mind.
Low barrier to entry and a simple, repeating mechanic are all you need to keep in mind when creating an addictive experience. With this knowledge, you too can create that next viral game that we all can't stop playing!