As I will have mentioned many times on this website, the vast majority of mobile games include some kind of deceptive implement such as in-app purchasing that reduces the fun and takes away all the game experience unless you pay real money. So here is a list of mobile games that are actually good and are not money grabs.
Pixel Dungeon (Free)
This is a challenging roguelike game (a turn based action strategy RPG) where you make your way through up to 26 levels of the dungeon to get the Amulet of Yendor. There are 25 types of enemies, 5 bosses, potions, scrolls, weapons, armour, enchantments and overall a lot of fun. The game is completely free and has no microtransactions, but if you like the game you can donate an optional £3 or $5 to support the developer.
Uniwar (Free)
This is a strategy game that you can play a campaign, solo mission or multiplayer with. There are 3 balanced character classes and you deploy troops using credits that are gained each turn and each troop moves a certain number of spaces per turn and does a certain amount of damage. The game's app store description actually prides itself on there being no pay to win. There are a few things you can buy but none are pay to win, they are mainly cosmetic.
Dungeon Quest (Free)