Colorful systems are associated with children while white has the broadest appeal.
The Wii and Wii U are both white because Nintendo determined that a simple aesthetic appeals to more ages. In an E3 interview with Game Informer, Nintendo's Shigeru Miyamoto explained, "We found over the years when we included a lot of different colors in our hardware is people would kind of point to that and use it to paint us as more kid-oriented."
He notes that previous Nintendo systems, such as the Famicom and Super Famicom, were far more colorful. The GameCube famously launched in purple and black. Miyamoto noted that while his preference is to "make greater use of color in our hardware," Nintendo has found that minimizing the number of colors maximizes appeal to all age groups.
Nintendo went with white for Wii and Wii U because they "found that rather than going all black - all white seems to have a broader appeal to people."