Wi-Fi is a very convenient way to allow your Pi to operate in a remote place within the wireless range. There are many types of wireless adapters available, and not all drivers are included with Raspbian. You might have to install a specific driver, but that is usually a simple process. However, when talking about wireless, you have to target the chip that is used on the adapter and not the end vendor who is selling it.
There is a comprehensive list of compatible adapters available at http://elinux.org/RPi_USB_Wi-Fi_Adapters.
One of the most stable and affordable chipsets is the Realtek RT8191, which works with the 802.11n standard. It is also compatible with the older 802.11b/g specifications, just in case your router does not support the newer 802.11n specification. It does not support 5 GHz frequencies or 40 MHz dual band though. Shop around to find the best price and don't be fooled by overpriced adapters that claim to be the...