Hashiwokakero (or Hashi for short) is a Japanese puzzle. I discovered it in the back of a magazine at my haircutter, of all places. Like sudoku, it's an abstract puzzle requiring reasoning about a number of constraints at once.
The numbered circles are islands, your task is to fill in the bridges connecting them. There can be zero, one or two bridges between each pair of islands, orthogonally. Bridges cannot cross, and the number on the island indicates the number of bridges to the island. Lastly, all the islands must be connected:
Indigo Puzzles has the nicest online implementation: not only can you interactively solve the puzzle, but you can ask for advice, and it will patiently explain a possible next deduction, and why. They have lots of puzzles if you join the site (free).