09/01/2015: A 22-pin WiFi module with 0.1" breadboard-compatible (or easily wireable) pads to break out essentially all the pins available from the SoC, not just a couple. Includes SPI flash and a user-defined LED (and power LED).
2.4 GHz antenna (microstrip inverted-F) and RF shielding can around the chipset are built in.
With an onboard regulator (12V max) and temperature sensor, and appropriate pull-up resistors on the enable and config lines, all you need to do after programming is simply plug 2 wires into a battery and you've got an Internet-connected temperature sensor ready to go, very simple and cheap, with no extra components, gateway or wiring needed to demonstrate a basic Internet-of-Things connected sensor application. Of course extra peripherals can be added to suit your needs.
This module will plug into a carrier board (not shown) with a neat USB UART for firmware updates and configuration. But you could rig up an FTDI cable easily if you choose.
If you want a simple Internet-connected temperature logging application, for example, you can just use the built-in temperature sensor - this is all the hardware you need, self-contained and ready to go. You don't even need the breadboard - just solder the two battery wires to the board.
But you've also got the option of using a breadboard if you want to prototype different hardware connected to the ESP8266.
I've left the shield off this one, for the photo, so you can see the chip inside.
(When I went to take this photo I couldn't find a 9V battery snap anywhere, so some improvisation was needed.)