A Wi-Fi project at Elektor-labs caught my eye.
The Wi-Fi module uses the AT command set through a serial interface.
When i read the article, i noticed the Wi-Fi module itself sells for a few Euros, and indeed, the lowest price i found on Ebay was about 7 euros (shipping included). Manufacturer info is available here. Additional info can be found on the web, just Google for ESP8266.
Seeedstudio also sells this module in different layouts.

Edit
As i didn't want to repeat existing topics, i searched the mbed site for ESP8266 before i posted this message. I found it quite odd no results were found even though this device is available for several months. There probably was a problem with mbed's search because a new search led to following topics on the site :
https://developer.mbed.org/forum/electronics/topic/5144/ (september 2014)
https://developer.mbed.org/questions/4993/How-to-interface-esp8266-wifi-module/ (october 2014)

Some additional links
AT commands
Forum

I noticed this one too. Looks very nice for IoT applications. Hope some one can enable it in Mbed SDK.

You dont need any enabling, it's as simple as Serial mydevice(txpin,rxpin); and then you issue AT commands to it like you would normally would to your pc terminal, like mydevice.printfn("").

Alltough there are may boards out there and some of them have all the IO/s mapped to header pins, you can only talk to it by uart. What would be nice is a SPI interface!

You can say the same aboth some others too, but a Socket implementation would of course be handy, to have it compatible with others.1

A couple of month ago i was trying to write a example port of this module to mbed, but then i notice that there was a SDK development for the module itself. Now it is realesed (http://bbs.espressif.com/viewforum.php?f=5) and i am just waiting for a suitable/nice/small/cheap development board.

However, there is the example code that i was writing (It is not tested so i am really sure that it won't works, but may it be usefull for anyone):

/media/uploads/jose_23991/main.cpp