My current setup is a Gumstix (single board computer with Cortex-A8 CPU and 256MB RAM) running Linux, so it's really just like connecting 2 PCs.
If you want to use microcontroller, though, some companies make modules that include wifi as well as the TCP/IP stack, and will allow you to talk to it like talking to an xbee (through UART).
If you have a more powerful microcontroller (eg. Cortex-M3) with a USB transceiver, it's probably possible to implement the TCP/IP stack in software (quite a few free implementations are available), and use a regular USB dongle. I'm not sure if a "driver" is available, though, or if not, how hard would it be to write one.
FTDI has a new chip that looks very promising. The FTDI Vinculum II. Basically a USB controller (dual ports host or client) with a microcontroller. They also have a lot of drivers already written (for HID, disk, still image devices, etc, and they also confirmed to be working on a driver for webcams/video class). I don't think they have a driver for wireless controller class, yet, though. Maybe it's not standardized enough to worth the effort?