Invented by AlexeyPajitnov in 1985, http://www.tetris.com/building_blocks/faq.html
Tetris was designed as an arcade version of the old pentominoes puzzle. In that puzzle, you would have shapes consisting of five attached squares in every possible combination, and try to make a solid square out of them. Alexey judged that these shapes were too complicated to use in an arcade setting, so he opted to use tetrominoes, which were shapes consisting of four attached squares.
In Tetris, the player controls a series of randomly-selected tetrominoes, which fall into a pit and form a stack. The game is over when the stack reaches the top. The stack can be reduced only by filling a solid line in the pit with blocks. More points are awarded when multiple lines are cleared at once, and when four lines are cleared at once it is called a Tetris. Small bonuses are also often awarded when the player opts to drop the block faster than it is falling naturally.
See TetrisAnalogy.
The early success of Tetris has spawned many look-alikes and variants, all based on the concept of shaped or colored blocks falling from the top of the screen. For example, there is HexTris?, in which the shapes are based on hexagons instead of squares; Columns, in which the shapes are simple lines but the point is to match colors; and various 3-d versions of Tetris. One of my favorites now is the shareware game Triptych, which is like Tetris with real physics: the shapes rotate, bounce, and jostle each other, giving the game a much newer flavor and a bit of addictiveness. http://www.chroniclogic.com/triptych.htm