You may remember an X-Men film from last year with the same name as this game, and they do tell the same basic story. The difference, however, is the game is true to the 1981 comic book story line and the movie is... well, not. X-Men: Days of Future Past is also a regular paid game with no in-app purchases.
This is a side-scrolling action title that gives you the chance to play as characters like Wolverine, Storm, Shadowcat, Colossus, Cyclops, and Scarlet Witch. You can upgrade and unlock new abilities as you play, and there's even a whole lore section of the game where you can read about the background of the X-Men universe.
You start the game in a dystopian future crawling with robotic Sentinels—the purple/pink ones, not those things from the movie. Then it's back in time to stop things from going wrong in the first place as you do battle in a variety of locations. If you like the classic X-Men stuff, this might be worth your time at about $4.