The original seven-string guitar appears to have been created in Russia sometime in the 19th century. Here is a short tidbit of information from a website detailing classical guitar history:
The invention of the seven-string Russian guitar has been attribution to Andreas O. Sichra (1772-1861). His seventy-five compositions for seven-string guitar became the nucleus of a rich literature for this instrument. He wrote an excellent method for the guitar.
Sichra's teaching methods and principles produced many of Russia's finest guitarists: Simeon N. Aksenow (1773-1853) who is among those credited with developing the use of harmonics; W. I. Swinzow who was one of the first seven-string virtuosi to perform in large public auditoriums.
Various other types of guitars may also have seven strings; there have been many very weird inventions and many unusual instruments throughout the history of the guitar. In fact, there is a particular guitar which has four necks and no less than twenty-four strings! Fear the luthier who designed such a monstrosity.
The realm of electric guitars shows a slightly different historical background. bluthunder supplies this description:
The seven string electric guitar had its origins in the 1930s, and was popularized by jazz legend George Van Eps. In 1938, he commissioned Epi Stathopoulo, president of the Epiphone guitar company, to build him his first seven string. Eps' 1931 Ephiphone Deluxe was then modified to accommodate a special 7-string neck. The 7-string has enjoyed modest popularity for over 60 years, and a recent demand for the extended low range of the 7-string electric has enticed a generation of new players to embrace it for its musical qualities. Its recent surge in popularity shows no evidence of abating.
pseen has a more modern story:
Introduced in the late 80's by Ibanez and Steve Vai, this electric guitar has an additional bass string, tuned one fourth below the standard tuning. The novelty of an extra string soon wore off though, and the Ibanez line of guitars was considered a flop.
The potential of these guitars was however recognized by a few musicians, in particular Swedish metal band Meshuggah, who have used the Ibanez Universe guitars exclusively since the early nineties. The seven string guitar, and the Ibanez line especially, have since been made more popular by American 90's metal acts Korn, Deftones and Fear Factory. So much in fact, that Ibanez reissued their line of 7 string guitars in the late 90's. A few other brands, like ESP, BC Rich and Schecter, also began making 7 string guitars as regular models (as opposed to custom models).
The conclusion we can draw from all this is that the concept of a seven-string guitar is by no means unique. It has perhaps been reinvented several times throughout the history of the guitar, a testament to the creativity and innovation involved in the use of this instrument.