The official Arduino WiFi shield is an easy but expensive option to get your Arduino on the wireless network.
But there is a cheaper nasty way that actually offers you lots more options.
A bunch of hackers have started re-engineering commercial Wifi-routers opening them up and updating the firmware to allow them to easily connect to the Wifi-routers with break-out boards like Arduino’s. The TP-Link TL-WR703N is a great example of a cheap travelers router that can connect to WiFi and includes a USB port.
Because the little router has an on-board USB port you can connect it to the internet with a 3G-USB stick. This also gives you the option to upgrade the connection to a 4G version in the future.
For more details on how to update the firmware on the TL-WR703N have a look at http://wiki.openwrt.org/toh/tp-link/tl-wr703n
The little router can also be used to turn USB devices into Wireless USB devices. Here is an example of a Wireless UP! 3D Printer being converted into a wireless 3D Printer.
Here are a few more links on how to connect and Arduino with this little router: