Successor hardware still planned for 2006. Updated with official comments from NOA.
Earlier today the Nikkei News reported that Nintendo would not be releasing a new home console. According to the report, Nintendo would instead continue to support the GameCube by releasing various peripherals and games. These accessories would take the place of a new console by improving the gameplay and furthering connectivity with the Game Boy Advance.
While the article begins by suggesting that no new console is planned, it goes on to say that one actually is planned, but will not be released for two to three years (around 2006). Satoru Iwata, president of Nintendo, has previously said that "customers are fully satisfied with the performance of the current model." Given various quotes from Nintendo, this was actually the plan all along. The company has said on prior occasions that they will release their new model around the same time as their competitors do. Both Sony and Microsoft have hinted at 2006 releases for their new consoles, so all of this falls perfectly in line.
If anything, this article only states that Nintendo will continue to support the GameCube while they are in development of a new console. There are no details on what these new accessories may be, but Nintendo has previously shown a portable LCD monitor, the SD memory card adapter, and other as yet unreleased add-ons for its system.
Update: After this article first went live, Planet GameCube received the following official response from Nintendo of America's Director of Public Relations, Beth Llewelyn:
"We are staying in the hardware business. We are working on a next-generation console and plan to launch it at the same time as our competitors. Nintendo has several hardware strategies for the future underway. In addition to the ongoing development of the next console, we are also considering accessories for the GameCube."
There is still no information on what those accessories might be, and Nintendo representatives did not indicate that an announcement was planned in the near future. We can only assume that something will be revealed at E3 in May.