Hitori
Shade the repeats. Keep the rest connected.
Erase repeated numbers from a grid without cutting the board in two. Ten puzzles per pack, endless custom puzzles, eight themes, no ads.
Three puzzles to play on your iPhone
The puzzles this blog writes about, made into calm, ad-free games. Each has a guided tutorial, ordered packs from easy to expert, endless custom puzzles and eight themes.
Nurikabe
Islands in the stream.
Numbers are island sizes; everything else is one connected wall. A guided tutorial, ordered packs from 5x5 to 10x10, and eight themes.
Norinori
Pure logic, domino style.
Every colored region holds exactly two shaded squares, and shaded squares pair up like dominoes. The region sizes are your only clue.