A wireless dongle will make your Raspberry Pi Wi-Fi capable, but only certain wireless adapters work with the Raspberry Pi.
What makes a Wi-Fi dongle compatible with a Raspberry Pi is the chipset that it uses. There are two chipsets that stand out as the most commonly used and popular.
2…Ralink RT5370 Chipset
These two chipsets are used in many adapters with different brand names and are known to work with a Raspberry Pi.
A second thing that must be looked at is the power that the USB on a Raspberry Pi can give to an adapter. Some adapters require more power to run and often a RasPi doesn’t supply the power that is needed.
For this reason nano wireless adapters or micro-USB adapters are used since they are small and have small power requirements.
For larger adapters with big antennas a USB hub can be used which will power the Wi-Fi dongle with its own electronics.
Recommended wireless N USB adapters
Wi-Pi Raspberry Pi 802.11n Wireless Adapter
Edimax EW-7811Un 150Mbps 11n Wi-Fi USB Adapter, Nano Size Lets You Plug it and Forget it, Ideal for Raspberry Pi / Pi2, Supports Windows, Mac OS, Linux (Black/Gold)
2.4 / 5 GHz Dual Band wifi adapter / dongle for Raspberry Pi
Tenda 300Mbps Dual Band Wireless N USB Adapter (W522U)