Subtitled "The game for the mind", this game definitely falls into the category of a brain teaser. Created by Pāvils Jurjān of Latvia, the game of Net is all about connections.
There is a central energy source, and the objective of the game is to connect all devices to the energy source in the fewest moves possible. Of course, if you're like me, I ignore the number of moves and just try to finish a puzzle. Connecting the devices to the energy source is as easy as clicking on a grid cell to rotate it. Rotating a cell costs one move, and you may rotate is as many times as you wish during that one move. Turn all red unpowered devices into green powered ones to solve the puzzle.
The game features high replay value due to its randomly generated puzzles. It is also highly customizable through many options that you can tweak to get just the right challenge for your taste and ability. For example, you may choose a play field grid of any size from 3x3 up to 13x11, in odd numbered increments. The game defaults to 7x7, and that seemed a bit too complex at first. I found that a 5x5 game is just about right for me. As an added challenge, you may also choose to play with borders that wrap around, which means that a powered wire on one side of the board can connect with a wire on the opposite side.
Thanks to Daniel for suggesting the game. He also suggests starting with the corners if playing a normal game, and if playing with wrapping he says you will need to begin with the sides. Net is an excellent mind bender of a game with features to fit every brain shape and size.