Just as Nintendo said goodbye to the Game Boy Advance era when it removed the legacy cartridge slot from the Nintendo DSi, the time has come to bid farewell to the GameCube as a new revision of the Wii hardware is on the way that drops support for everyone's favorite cubical video game console.  Kotaku reports on the next phase of the Wii:

The change is that this Wii is designed to lay flat and has a slightly reconfigured design. The original Wii was supposed to sit vertically. The upcoming Wii U console sits flat, so the tweak could be to bring cohesion between the two machines. Or it could bring confusion.  The biggest difference is that this console cannot play GameCube games like the current Nintendo Wii.

This shouldn't be too much of a surprise.  All of Nintendo's successful hardware has been revised late in its life to become cheaper to manufacture and more cost effective to sell.  Sometimes useful capabilities are lost in the process (most often it's an unsupported expansion port that is removed from the design, but sometimes support for certain kinds of video cables ends up tossed away as well).  While we'll all miss GameCube games, they won't be gone for too long.  Word has it that Nintendo expects to reintroduce some of them as downloadable Virtual Console titles for the Wii U.