There are 3 games prior to this from what I understand: 7th Dragon (on DS), 7th Dragon 2020 (PSP), and 7th Dragon 2020-II (PSP). I've only played 2020-II, I was drawn in at the time by the interesting art style and wanted to bite straight into the latest title. I definitely should have gone in order, because the first two games have been sitting unplayed on my backlog since then. I'm especially interested in the first game on DS since it's not set in Tokyo like the next two - actually, I heard there's an English fan patch out for it as well. I'm sure a lot of people reading this know much more about 7th Dragon than I do.
7th Dragon 2020-II was a charming game that had a hilariously cheesy plot involving the U.S. being up to no good and being arrogant underhanded pricks until they were finally taught how superior Japan is at dragon killing. It ended with the U.S. special forces playing a supporting role to the true glorious nipponese heroes defeating the invading dragon leader, it was so wonderfully campy. I took a quick glance at the plot outline of the first 2020 game and it also apparently had America being jerks, so I'm really looking forward to seeing if the tradition of tsundere game developers with something to prove continues in 7th Dragon III Code: VFD.
The game seems to have recycled an awful lot of assets from 2020, but some models have been improved and it definitely seems like the character classes have been given more depth, so I'm looking forward to it.