Phil Are Go! has unearthed this 1963 advertisement for "broadband" data services from Western Union: "So, by 1963, business guys who were rich enough to have those little egg cups could transmit pictures, charts, stock data and stuff over the phone lines. Who knew? Well, the internet knew. It's just jarring to see the word "broadband" appearing in print as early as the sixties. I tried to find some numbers on what qualified as broadband back then, but couldn't find anything. Shazbot."
I don't know what 1963 considered "broadband" either, but I'm guessing 300 baud?