During the Curso de Arduino UFRJ (an Arduino course at Universidade Federal do Rio de Janeiro the students had the idea to control an AC light bulb using Twitter, so we developed this little projects in near 1 hour!
The project have a simple architecture as follows:
[PC with Python program] <--- USB ---> Arduino <--- relay module ---> AC lamp
This software does a search in Twitter and, based on the last tweet it find, send a message to Arduino via USB with what should be the state of the lamp.
Just receives the command from Python software and turn HIGH or LOW the digital port 13.
You could attach everything to the Arduino that can be controlled by Twitter. In our experiment we attached a relay module to the digital port 13. Then, the relay module activates or deactivates the AC lamp.