Sudoku
Solve the puzzle by placing numbers on a grid so they don't repeat -- sounds simple? try it!
(external)

Word games
Try to clear the board by forming words and maximizing the score -- think Scrabble or Boggle.
(external)

Lines
Move dots to form groups of 5 or more on a grid.

Reversi (aka Othello)
Play against the computer by placing white or black disks on the board and flipping your opponent's disks trapped in between.