As seen in theTweet Like Don Draper article by Design Taxi, two digital firms have created Tweephone, the first analogue Twitter client. It looks like a retro rotary phone, and uses old-school texting methods (hit 1 once for A, twice for B, etc). Except, you have to dial these letters in, obviously. A bit time consuming, but interesting.
And you can follow tweets from this phone by checking out their profile.