According to Shigeru Miyamoto, speaking with news.com.au, you'll likely only be able to use one of Wii U's fancy new touchscreen controllers on the system at a time — which explains the reports circulating yesterday that the controller would not be sold separately.
"Our basic premise is that you can use one with a system," said Miyamoto. "If we got to an idea of having multiple, it might be just more convenient for people to use their Nintendo 3DS and have a way to connect that. That being said, we are doing research about if someone brings their controller to their friend's house and they want to play together on Wii U to whether or not something like that would be possible."
Part of the reason behind this may be the fact that even with the Wii U's enhanced processing power over its predecessor, there might still not enough there to run more than one of the controllers at once. During the reveal of the console, it was explained that the image on the screen of the controller was actually generated by the Wii U base unit and transmitted wirelessly to the controller, rather than the controller containing its own standalone processor and graphics hardware. If this is the case, then using multiple controllers would put a proportionally-greater strain on the Wii U system.
Players who don't use the Wii U-specific controller will presumably be relegated to Wii Remotes, Classic Controllers or equivalents. And the tech demos on display at E3 show that it's possible for the Wii Remote-wielding players to have a very different experience to the Wii U controller user — not necessarily a bad thing. Games will presumably, then, be designed with this limitation in mind.