The 140 character limit is so that Tweets can fit in a 160 character SMS, with space left over for a username. SMS was originally a popular way to use Twitter. (And I think you still can?)
SMS is actually 140 octets, but the GSM 7-bit encoding that's typically used means you can get 160 characters. If you use characters outside that set, its switches to 16-bit UCS-2 so you are limited to 70 characters.
In reality you can send messages longer than this and they will be split into multiple messages over the wire - however in the US where you had (have?) to pay to receive messages it meant you would be charged for each individual message.
TL;DR; These limits may have made sense for the MVP, but as soon as most people moved to IP clients they were obsolete.
"SMS was originally a popular way to use Twitter."
I use SMS->tweet all the time. There is also a set of commands you can use over SMS to talk to twitter. [0] Doing so makes more sense (to me) as SMS is a reliable protocol over mobile networks.
Well, one of the big benefits of SMS twitter was you could subscribe with no account. We used this for our systems notification twitter account to send out status updates during downtime or any time when we were pretty sure our user base couldn't access our status page through normal means.
Mildly annoying was at the time there wasn't a way to see how many SMS subscribers you had. Don't know if that has changed or not, but it left us constantly wondering how many we had outside of our IRL headcount.
