Zigbee is a wireless communication protocol like bluetooth right? The only experience that I have had with that is through some of the Zigbee functions built into certain Microchip PICs. If you are looking to build a circuit using Zigbee you could start there for a microcontroller.
Ya, you are right I guess I didn't mean "built in" but I meant that it's easy to use the PICs with Zigbee systems. If you want to try a low price demo board just to play around you can try something like this:
Freescale (Motorola) is pushing Zigbee very hard. Go see their web site. There's also zigbee.org where you can get some docs, but they are not a non-profit organization.