I just found an awesome app (Android and iOS) called Blynk that allows you very quickly and easily connect any Arduino board to the internet. It took for me less than 5 minutes to control my UNO with official W5100 Ethernet shield via my smartphone (wi-fi, USB also supported).
Getting started instructions are very simple. You need just install library, upload correct sketch and put your token.
Here is how final setup could look: