Quoting Squill

I wanna hear the technical mumbo jumbo

Okay, here goes... (Note: previous poster was nearly there, but not quite)

Since Bluetooth is a wireless medium, all devices that use it must share the same medium (the air), unlike wired devices which have their own personal medium (for the most part). It uses a system called frequency hopping spread spectrum or FHSS, simpy a method by which the Bluetooth device can differentiate between all the different Bluetooth devices. Different devices will communicate on different frequencies at different times. In order to know what these times and frequencies are, they must be told by the 'master' i.e. the Wii. Thus the need for a sync for new controllers, but not for the packaged controller. I would be very surprised if the 360 didn't also need something similar, I don't know what it uses though.

The number of addresses is actually much smaller than suggested by the previous poster (only 8!). One of these is the Wii (master) and the others are for Controllers. So technically you could have up to 7 controllers on the Wii, but i'm not sure if Nintendo are supporting that (I don't see why not, it would be extra effort to stop people from using 7).

Using an unsynched Wiimote won't affect others Wii's though, your Wii just won't be able to see it. To wrap up, the 'address' referred to by the previous poster is likely the Service ID, which tells other Bluetooth devices what kind of service the Bluetooth device is offering. In this case, all Wii controllers will have a unique ID saying 'Hey everybody, I'm a Wiimote!'. Wii's will likely ignore devices with other service IDs, but nothing can be done too stop other masters finding Wiimotes and receiving data from them...*

*For anyone who's interested, google 'Wiimote mouse' and check out the Youtube video (sorry I can't link yet...)