To the gamer who does not understand the history of animation:2D games represent the past and 3d games represent the future.
There is some truth to this but the reality is not as black and white.
Computer graphics evolved with both 2d and 3d schools parallel and complementing the other. From the early days of the 60's in the research labs to the computer labs of the 70's and to the home TV screens of the 80's, computer graphics has evolved at rates that surpass Moore's law. It is true that 3d graphic power of home gaming system is growing at an alarming rate but the popularity of 2d games has shifted to a more specialized environment.
The success of the Gameboy Advance enables a platform for innovative and modern 2d game development. I am going to look into my crystal ball and predict that the next generation of Gameboy hardware will be backward compatible and feature a powerful enough CPU and memory to enable 2d games as complex as the Sega Saturn and 3D as powerful as the PSOne. World wide the Gameboy Advance is beating the PS2 in software sales. That really does not matter because the are not in direct competition just like 2d is not the enemy of 3d graphic systems.
The smaller screens of portable game systems, cell phones, PDAs and web games are better suited for 2d graphics. To establish a 3d rendering engine on a CPU and screen that is much smaller and less powerful than a main stream console system would be like trying to build the Titanic in a glass bottle. 2D graphics deliver a higher complexity of game play to CPU and memory ratio. They get more miles to the gallon if you will.
99.99% of the web is 2d graphics and the majority of TV and Movie animation is 2d. The chance that 2d is going to go away is no more than the chance that retro joysticks with Atari 2600 systems are going to put Sony out of business.
2d and 3d graphics are two sides of the same coin and they are both brushes to be wielded by the game designers of the future. I am optimistic and believe that the best 2d games have yet to be seen. Video games are to new of an art form to limit what they can be.

Brian Clevinger wrote an essay on old skool vs new skool. It might have some relevance to the whole 2D debacle..
http://www.nuklearpower.com/oldvsnew.php
I have also heard about 4 d