League of Legends
I think that the reason for the game's popularity is its balance between individual player impact and necessity for strategic decision-making. It manages to make individual players feel like they are all-powerful team-killing machines, while at the same time always requiring them to depend on their team in order to win.
The necessity of strategic decision-making is also what frustrates so many players. When this necessity arises, players are either oblivious to what decision needs to be made, or unable to communicate to their teammates of the best course of action in time for it to matter. A player that feels powerful can completely lose a game due to unfortunate situations and ignorant teammates. This results in an environment of constant adrenalin and disappointment, a combination that cultivates addiction.