The following Channel Guide will help you:

Determine best shields to use for your wireless Arduino project (WiFi, Bluetooth, NFC, or GSM Cellular).

Check compatibility of your adapter and its range compared to its competitors.

Compare prices and hunt for cheapest and most reviewed options on the market.

At the bottom of the page is also a list of tutorials and projects for reference.

Arduino Yún: $69

Description: "Arduino Yún is the combination of a classic Arduino Leonardo (based on the Atmega32U4 processor) with a Wifi system-on-a-chip running Linino (a MIPS GNU/Linux based on OpenWRT). It’s based on the ATMega32u4 microcontroller and on the Atheros AR9331, a system on a chip running Linino, a customized version of OpenWRT, the most used Linux distribution for embedded devices".

WiFi Shields:

XBee

XBee® Wi-Fi - Embedded Wi-Fi module for OEMs

A popular choice the Xbee modules are "Ideal for energy management, wireless sensor networks and intelligent asset management, the XBee Wi-Fi offers 802.11 b/g/n networking and flexible SPI and UART serial interfaces. Because the module includes the 802.11 b/g/n physical layer, baseband MAC and TCP/IP stack, developers can add Wi-Fi to their products simply by connecting to the XBee Wi-Fi's serial port."



Description:The XBee ZigBee modules from Digi International are available in two major classifications: XBee Series 1 and XBee Series 2 modules. The Series 1 and Series 2 modules are quite similar, but selection of a module should be based upon application specific needs

- See spec differences here

Bluetooth

Arduino BT Board: eur 79

Description: It supports wireless serial communication over bluetooth (but is not compatible with Bluetooth headsets or other audio devices). It has 14 digital input/output pins (of which 6 can be used as PWM outputs and one can be used to reset the WT11 module), 6 analog inputs, a 16 MHz crystal oscillator, screw terminals for power, an ICSP header, and a reset button.

Web Urban Blue Olive: $63.99

Description: Blue Olive connects via the regular Olive pinouts on the Magnolia and Oak boards and provides BlueTooth Class 1 (range 300 feet, 100 meters) connectivity to your projects. Since it uses the standard USB pin configuration, swapping out our Olive for the Blue Olive is easy and convenient. Clearly marked pins and Arduino compatibility means it will work for your custom projects as well.

JY-MCU Arduino Bluetooth Wireless Serial Port Module: $8.60

- Instructable: Androino! Control an Arduino from your Android device using a cheap bluetooth module.

Bluetooth Low Energy (BLE) Shield for Arduino

RFDuino

BLEDuino

Ember & Torch

RF

Arduino Ethernet Shield:

Description: The Arduino Ethernet Shield allows an Arduino board to connect to the internet. It is based on the Wiznet W5100 ethernet chip providing a network (IP) stack capable of both TCP and UDP.

-An Atlas of Arduino Ethernet Shields from Rob Smallshire for more details of each version

Other ethernet based options can be found here.

Using a router:

Using OpenWRT (Described as a Linux distribution for embedded devices) is another alternative to a typical shield that can be quite cost effective (Example is GL.iNET GL-MT300N-V2 Mini Travel Router for $21, OpenWRT wiki on it can be found here.).

Tutorials and Projects:

Sparkfun did a good write-up that breaks down these technologies (wifi, bluetooth, RF, etc) by costs, data speed, learning curve and size.

Presentation: Arduino and the real time web - By Andrew Fisher

Teleduino "converts your ethernet enabled Arduino into a powerful and versatile tool for interacting with devices over the internet."

Nanode: $39

Description: "An open source Arduino-like board that has in-built web connectivity. It connects to a range of wireless, wired and ethernet interfaces. It allows you to develop web based sensor and control systems - giving you web access to six analogue sensor lines and six digital I/O lines. Note: 802.15.4 based, compatible with most Arduino shields and software and has three connectivity ports Ethernet and Wired Serial" OpenPicus: See: FlyPort smart Wi-Fi 802.11 module

Description: "An open source embedded platform for Smart Sensors and Internet of Things. Each openPICUS module combines Processor power and Connectivity (Wi-Fi, Bluetooth or LAN).You can easily develop and run applications on modules using the free IDE - no Wi-Fi expertise is needed - openPICUS framework, based on freeRTOS, keeps the control of the Wireless stack and its events, leaving you free to concentrate on your application." Netduino Plus: $60 Description: "Does not have wireless built-in and must be outfitted with a module. An open source electronics platform using the .NET Micro Framework. Featuring a 32-bit microcontroller and a rich development environment, it is suitable for engineers and hobbyists alike. The Netduino Plus is just like the Netduino, with Ethernet cooked in. There is a full TCP/IP stack with examples ready to go, and a microSD card slot for storing files." See a list of more popular Internet of Things prototyping hardware.

Related: Raspberry Pi Wireless Options