Is it possible to use XBee modules as a stand-alone module without connecting a host MCU?

Applications based on Xbee modules are usually connected to a host MCU which is usually Arduino, based on what I have seen on internet forums so far.

Is it possible to have applications using stand-alone Xbee modules without connecting a host MCU?

The programmable XBee variants have a co-processor on the module itself. Freescale HCS08 with 32K Flash, 2K Ram.

Programmable XBee-PRO ZB Dev Kit

Sure it is. It is just a matter of what you want to do, what functions you require and which XBee module you need.