Depending on your interests, there are many great free apps available for both android and iOS. If casual games are your thing, then the extremely popular Candy Crush Saga, or Diamond Digger saga might be for you.
In the simulation genre you have interactive games such as Clash of Clans ( a virtual combat strategy game) or Hay Day (a virtual farming game) to entertain you for hours and hours. I would warn you, though, that these games take up large amounts of memory, which might need to be taken into account.
Kill shot is a very popular shoot em up style game, while Bike Rivals may be the best racing game around currently.
Moving onto sport games, GolfStar is a great golf simulator, with FIFA15 UT proving to be a great game linked to the console version, focusing on the Ultimate Team gameplay mode.
Classic arcade games are not consigned to history, either, with Subway Surfers, Sonic Dash and Despicable Me Minion Rush all fulfilling the 'runner' style of game more than admirably.