If you wanted something a little more cutting edge than the classic titles that Game Pigeon offers, there's no shortage of awesome iOS titles with really unique premises that have recently debuted.
War Tortoise 2 is a super compelling game that doesn't take itself too seriously. Yes, it's about war and destruction, but your character is literally mowing down enemies while sitting atop an enormous reptile that you can upgrade. Want to protect your huge animal with more stalwart armor? No problem, bigger, badder, and better guns? Go nuts.
If you like more cerebral experiences with an emotional feel, check out If Found..., which tells the story of a Kasio, a woman who returns to her hometown in Ireland and immediately has to deal with drama between friends and family. Before she has to process all of that fun stuff, a Black Hole comes to threaten the world.
Kasio has to stop the threat from engulfing the planet in this hand-drawn title that costs $5. Sure, it isn't free, but it isn't spoiled by ads and it's evident that the developers worked really hard to make a super special title. Animal Crossing: Pocket Camp, is also really cool, and if you like RPGs, try Disney Sorcerer's Arena or Undead Horde.
Honestly, there are tons of great titles you can check out, but those are some of the most notable ones from this year so far.