Do you need a wireless adapter for wireless connection?

I will make the assumption that you are referring to setting up your Xbox 360 to the internet to take advantage of the LIVE features. Microsoft has yet to sell an XBOX with a wireless adapter pre-installed with the console itself. Instead you must buy an adapter piece for the XBOX.

Here are two links for buying the adapters for your console:

Amazon.com/Xbox-360-Wireless-Network-Adapter-Networks/dp/B000B6MLV4">http://www.Amazon.com/Xbox-360-Wireless-Network-Adapter-Networks/dp/B000B6MLV4

http://www.xbox.com/en-US/hardware/x/xbox360wirelessnnetadapter/