Kotaku held an interview with Shigeru Miyamoto at E3, which has yielded some interesting responses.
The capability for Wii to connect with DS is built into the system, but they have not yet decided how to use it fully. Miyamoto suggested that they would use the touch screen and the microphone to interact with Wii titles, or users could download things to the DS, edit them and upload them back to Wii. While they don't have anything specific planned yet (that they want to talk about, anyhow), it is expected that DS and Wii connectivity will be present either upon launch or close to launch due to the resounding success of the handheld system.
On a more intriguing note, Miyamoto mentioned that Wii remotes can be linked to different members of the family with their own settings attached to each. Nintendo are hoping that each member of a family will have their own remote to use with the system, so that the system can adjust its settings automatically depending on which remote was used to switch on the system or join a game.
Miyamoto also mentioned that the price and launch date were not specified at E3 due to them wanting to focus on the hardware and software. He believes that pricing details will probably be announced later this year at the Tokyo Game Show.
Stick with C3 for more from E3 as it comes!