Top 10 Games

1. Bulletstorm - This game has a story in which the main protagonist seeks revenge for being forced to kill good people and so, crashes his ship into a planet full of mutants in a failed attempt to kill him.
2. Dark Souls 1 - This game has a simple story in which the main protagonist must prevent the age of darkness by sacrificing their soul to the first flame in existence.
3. Blade and Soul - This game has a story in which the main protagonist seeks revenge on the people that murdered everyone they know. 
4. Warframe - This game has a story in which the main protagonists, ancient warriors known as the "Tenno", have awoken from cryosleep during a planetary war and must fight back.
5. Binding of Isaac: Rebirth - This game has a story in which the main protagonist Isaac escapes from his overly-christian mother who is asked by god to kill him.
6. Magicka: Wizard Wars - This game has no story and simply involves wizards fighting each other.
7. Smite - This game has no story and simply involves gods from all pantheons battling.
8. Gauntlet: Legends - This game has a story in which a mage called Garm summoned the demon Skorne who then imprisoned his soul in the underworld and so, the main protagonist must fight through a tough gauntlet to save him.
9. One Finger Death Punch - This game has no story and simply involves fighting endless amounts of enemies in fast-paced strategic combat.
10. Metro 2033 - This game has a story in which the main protagonist Artyom must make his way across a post-apocalyptic Moscow to destroy the base to an alien race called the "Dark Ones".

Nearly every game in existence has some kind of story, whether it's very simple or incredibly complex, it's there. Though there are some games that have no story whatsoever. Here are a few examples:

     Tetris (Puzzle)

     Worms Series (Action-Strategy)

     Wii Sports and Wii Play (Sports/Party)

     Monster Hunter (Action-RPG)

     Zynga Poker (Card/Poker)

When creating a game the developer will look for a balance between story and gameplay. If a game has very fun and addictive gameplay then a story might not be required. But a game that has hardly any fun gameplay elements might need a good story to save it from failing. The most common genre to have no story are puzzle games as their core is gameplay and a story isn't important. These kinds of games are commonly played by middle-aged women during breaks at work or at many different times at home, though people of other ages have been known to play them too. The main reason that people play puzzle games is for the competitive elements. Friends who play the same game will feel obligated to get to a higher level than the other and thus have the potential to play the game for several hours per day.