By the time the third game came out, the anime series had almost reached its conclusion, so the initial trilogy followed all story arcs in the series, from the arrival of Radditz on earth to the battles against Majin Buu, with Hyper Dimension released several years down the line after the end of the anime, very late into the life of the Super Nintendo, wrapping things up with the Kid Buu story. The first three games were produced as the anime series was going strong in Japan, with each iteration following several story arcs of the plot already aired in Japan so far. Now, all these years later, and after a brilliant, yet, sadly, Japanese-exclusive Nintendo DS iteration in the Butoden series with Dragon Ball Kai: Ultimate Butoden, the series comes back to grace all regions of the world on Nintendo 3DS. Nevertheless, it helped introduce non-Japanese audiences to the joys of throwing massive attacks, pretending to be Goku and co. All of those games were released in Europe, but exclusively in French speaking regions and Spain, albeit in badly translated form. Three Super Butoden games were produced, as well as Dragon Ball Z: Hyper Dimension. The latter saw no less than four different fighting games based on the "Z" anime series, which was still being aired in Japan at the time, as the Super Famicom was the most popular platform in the Land of the Rising Sun.
The franchise got adapted into lots of different kinds of media, and this included video games on the Famicom, and then, subsequently, on the Super Famicom.
It took its time to be properly adapted in English, but, meanwhile, it was also enjoying quite a bit of success in the French speaking parts of Europe, as well as Spain. From the manga that started it all, very loosely inspired by the traditional Chinese story Journey to the West, to the even bigger anime adaptations of the books. Anyone knows how big Dragon Ball is over on its home turf, as a licence.