A great article about Twittering with Mathematica on the Wolfram blog. I had investigated a while ago a Mathematica twitter bot for doing “Micro-calculations” with the results from Mathematica being less than 140 chars. Not very useful but a fun bot.
Anyways if you are interested, I made a gist for it. Its in Java and uses JLink to communicate with Mathematica. It was never running for long as I suspect it violated some end user license, but basically one would send a Mathematica command to @mathematica and it would tweet you back your result evaluated by the MathKernel. I am hoping Wolfram might create a similar bot themselves for when you need to know the value of a special function quickly 
That is a very good idea! It could be used if you are running a long calculation that takes weeks but every now and then it gives you a point/result that you could publish real time!