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:
http://www.Amazon.com/Xbox-360-Wireless-Network-Adapter-Networks/dp/B000B6MLV4
http://www.xbox.com/en-US/hardware/x/xbox360wirelessnnetadapter/
wireless router
You will need a wireless router and a wireless adapter to have wireless pc to pc connection
If you want to use wireless connection yes you need a wireless adapter.
Wireless adapters (USB or not) are good for connecting to wireless networks (aka WLAN or WiFi).
you ether need a Nintendo wifi usb connector or a wireless router.
The Wireless adapters should not be required for computers because they are not mobile and have better connection with the Ethernet. Netgear is the most popular type of adapter and is recommended only for laptops.
You need a WiFi connection to the internet to be able to use the wireless connection in the PS3. For people without one and that already have an internet connection they can purchase a wireless router and connect it to the modem. You can also purchase a router and an ethernet cable and have a wired connection to the internet.
You need to get a wireless adapter for that, either external such as USB, or internal such as PCI, PCI-E and so on.
A wireless USB adapter allows a computer or wireless device to connect to a wireless router. It is needed for any device which is not wired to an internet connection, to connect.
A usb wireless adapter is useful to obtain a wireless connection on older computers or when an internal wireless card is nonoperational. It can be an easy fix instead of having to take a part ones computer.
You need a wireless connection to connect, then you buy xbox live in a gaming store. Good luck with your connection.
For a wired connection you need a high speed modem. For a wireless connection you need a wireless networking adapter for your 360. Or perhaps you need a new router, as some are incompatible with the 360 console.
With an Ethernet cord or a wireless adapter.