Arrow Puzzle (Easybrain)
Tap arrows off a crowded grid in the right order, without hitting a blocked one.
Every day: Daily Challenges: a puzzle for each day of the calendar, with monthly challenges that award trophies. New puzzle: Once a day; the App Store listing does not state the time.

Arrow Puzzle is Easybrain's tap-away logic game. The board is a maze of arrows pointing every way; tap one and it slides off the grid if its path is clear, but a blocked arrow costs a life. Besides hundreds of levels, Daily Challenges give a puzzle for every day and monthly trophies.
Games like Arrow Puzzle (Easybrain)

Arrow Escape (Puzzleship)
The same tap-away arrow puzzle as a daily web game.

Sudoku.com
A classic nine-by-nine sudoku for every date, with a calendar archive and trophies for the daily challenges.

Blockudoku
Drop blocks on a 9 by 9 grid and clear lines and squares to hit the day's target score.

0h n0
Place red dots so every blue dot sees exactly its number, with a fresh set of grids each day.

3Doku
A sudoku wrapped around a cube, using the numbers 1 to 16.

alikely
Tap the emoji that share today's hidden connection before your lives run out.

Amsterdammed
Draw one canal loop through every open square of an Amsterdam grid, around houses and windmills.

ARCaptcha
Work out the rules of a tiny unexplained game by playing it, one game a day.