You might want to specify that you're looking for android games in the title, "smartphone" isn't very specific
Fruit Ninja
Pretty sure everyone has heard of this one but you slice fruit as it flies up on screen, avoiding bombs while making sure fruit doesn't fall off screen without being sliced (there are score attack modes, too), has payment options to make things easier/quicker but you can do everything without spending a cent
Temple Run 2
Quick-time-event-like game, unfortunately requires either a lot of grinding or incredible skill & luck passed a certain point if you don't want to pay
Jungle Heat
Semi-online game, build a military base to prevent players from stealing your resources while creating an army to return the favor, also has single-player campaign options
Pixel Dungeon
Roguelike modeled after Brogue, features low-res graphics instead of ASCII and is naturally tough as nails
Meteor Blitz
Paid, twin-stick space shooter, basically Asteroids with upgrades and enemies
Radiant
Paid, Galaga on steroids with neon Space Invaders graphics, multitudes of different upgradable weapons
