Los Angeles Times has an article on why text messages are limited to 160 characters. Read the abstract below.
In 1985, Friedhelm Hillebrand of Bonn, Germany and a dozen others had been laying out the plans to standardize a technology that would allow cellphones to transmit and display text messages. Because of tight bandwidth constraints of the wireless networks at the time, each message would have to be as short as possible.
Hillebrand has conducted an informal study using his typewriter on how many characters are required on an average to express a sentence or question, by typing out random sentences and questions on a sheet of paper. He counted the number of letters, numbers, punctuation marks and spaces on the page, and came to a conclusion that each blurb ran on for a line or two and nearly always clocked in under 160 characters. That became the magic number which set the standard for one of text messaging.
Friedhelm Hillebrand was the chairman of the nonvoice services committee within the Global System for Mobile Communications (GSM). He pushed forward the group’s plans in 1986 and all the cellular carriers and mobile phones must support the short messaging service (SMS).
The committee took the assumption based on other two factors: For one, they found that postcards often contained fewer than 150 characters. Second, they analyzed a set of messages sent through Telex, a then-prevalent telegraphy network for business professionals. Despite not having a technical limitation, Telex transmissions were usually about the same length as postcards. The committee finally decided on the 160 character length for text messages.