The World's First Cellphone
As the above photograph should indicate, AT&T was testing radiotelephony as early as the mid 1920s. Radiotelephone service was introduced soon thereafter, and starting in the 1950s, it was not uncommon for the senior executives of major corporations, as well as other people of importance, to have radiotelephone setups in their care. With these systems, you'd pick up the handset and would be automatically connected to an operator, who would then route your call over the phone network to whomever. You could also accept incoming calls. The modern cellphone networks were merely a logical refinement of this technology.
That said, the
design of the flip-phone type cellphones popularized by Motorola in the late 1990s could well have been influenced by the ST communicator (specifically, the flipout action by which you extend the phone when answering it), as product designers often get inspiration for various features from unusual sources. Considering that many consumers prefer "candy-bar" phones to flip-phones, this accomplishment is nothing for ST to be that proud of, neccessarily.
That said, I've always liked Captain Kirk's TabletPC (being an avid user of that technology). However, its also worth noting that Star Wars featured what may have been the first PDA-a handheld device being used by an Imperial officer in TESB. Note that I do not consider the Tricorder to be remotely akin to a PDA, as the Tricorder was basically a handheld scanning/sensing device used for scientific and medical purposes, as opposed to a general purpose computing device used for e-mail, organizing, word processing, websurfing, et cetera. (One also can't help but wonder if the Imperial officer doodling on his PDA in ESB was actually posting to his Myspace blog.)
"Here's a nickel, kid. Get yourself a better computer."