The first generation of video games were all two dimensional. The internal representation of the game world had only two axes at most (usually up-down or left-right). Some games, such as Diablo, tried to give the illusion of depth by using isometric perspective, but it was all make-believe.
Two-dimensional games are mostly gone from high-end platforms such as PCs and consoles. However, there are many other uses of two-dimensional technologies, which still remain today. Handhelds, game-capable telephones, and even interactive television are only some of the scenarios where 2D is still the way to go. Moreover, the strict limitations imposed by the 2D programming rules are a good exercise for any modern game programmer. Many of the optimizations and techniques found in 2D titles are still used in higher-end platforms today.