Admittedly, it's not the plane itself doing the Tweeting: it's the airline. Lufthansa has set up a new service named MySkyStatus that automatically posts the current position of your flight to Twitter or Facebook so your friends can follow your travels (and your friends living in those cities can look up!).
Typical status updates read "flying over San Francisco Intl, California 94030, USA on United Airlines" or "flying over Grantsville, UT 84029, USA on United Airlines". It seems the system posts the flight's position around once per hour, pulling info from a database of flight information.
Here's the really smart bit: I stumbled on the service because one of my Facebook friends was on a United Airlines flight today. Clicking the link in the update, of course, directs you to the Lufthansa MySkyStatus page with a Google Map of the flight's position, meaning that Lufthansa is getting free social media promotion from people travelling on all airlines. Pretty smart.
On a long haul flight, of course, the system may post 20 updates or more, but the functionality is so cool that I'm prepared to give some slack to those Twitter and Facebook friends who have decided to put their updates on autopilot.