Why 140 characters? The obvious answer, which I'm sure you know, is so that a tweet can fit into the 160 character limitation of an SMS text message. In other words, the Twitter user name (which can be up to 15 characters) followed by the 140 character tweet can all be packaged nicely into a single SMS text message.
Which begs the next question: Why restrict a tweet to the limits set by SMS when this is the World Wide Web? One of the "limitations" of e-mail and the Web is that you need Internet access for connectivity. In developed countries, we take Internet connectivity for granted. Having spend some time living in East Africa I was amazed to see how important SMS was to the locals who don't own computers, printers, or even have an e-mail address. But, nearly all of them had pre-paid cell phones and they used SMS just like we use e-mail (they also had trivial SMS to e-mail and e-mail to SMS bridges).
Additionally, their cell phone networks have features which I wish we had here in the US. Basically, people in developing countries have substituted the computer, printer, and Internet with the cell phone, fax, and the carrier's wireless network. This is how most of the world gets "online" with technology.
Imagine if Twitter didn't just go after the consumer market who own computers and smart phones with Internet access (I'm guessing about one billion people), but, instead, what if Twitter went after every person on the planet who's an active cell phone subscriber (which will reach 4.6 billion by the end of 2009). Now, that would be a fantastic communications tool!