I've found the ESP8266 while I've been looking for a wifi interface for my simple Arduino IoBot project http://iobot.info/. The fact that it can run Arduino sketch stand-alone was positive surprise for me so I redesigned the robot this way and I would like to share it with you:
All the files as well as sketch for Arduino IDE are available on my GitHub: https://github.com/zygmuntw/IoBot There is also manual on Instructables.com: http://www.instructables.com/id/How-to-make-a-DIY-Mobile-Desktop-App-Controlled-3D/, it is for the Arduino Uno version but most things are same.
I did found that on standard install of Arduino IDE board manager servo library is not going to work so according to this post: https://github.com/esp8266/Arduino/issues/8 when you setup Arduino IDE enter "http://arduino.esp8266.com/staging/package_esp8266com_index.json" into Additional Board Manager URLs field.
Now don't forget to put your wifi ssid and password in to the sketch before you upload it:
char ssid = "--------"; // your network SSID (name)
char pass = "--------"; // your network password
Then after upload, when you still connected with serial you will get the IoBot IP from serial monitor:
Put the IP into the IoBot App settings:
And you are ready to control the robot:
If you have any question, please don't hesitate to contact me.