There are 8 Wizardry games in the main series, plus the spin-off Nemesis. There's also Wizardry Gold, which is just a buggy, half-hearted Windows version of Wizardry 7.
Wizardry 1-3 use the same game engine, but I don't think you can transfer characters. The stories are totally different anyways.
Wizardry 4-5 are the same deal (their engine is newer though).
Wizardry 6, 7, and 8 are a real trilogy (well, 7 and 8 built off of the end of 6 anyways), and you can transfer characters (via saved games) from 6 to 7 and 7 to 8.
Nemesis is a terrible attempt at a first-person adventure game that spans something like 5 or 6 CDs. I don't know what it has to do with Wizardry, as it certainly doesn't seem to have any of the world, story, magic, or any other elements from the other games (6 through 8 anyways). I never got far in that game without losing interest. You pretty much just wander around from pre-drawn scene to pre-drawn scene looking for items laying on the ground to solve puzzles, and I think there's some uninspired button-smashing combat thrown in as well.
I should mention that I never got into Wizardry until part 6, so I only know of its predecessors through more recent research. In my opinion, the technology leap and lack of story connection between Wizardry 6/7/8 and the first five make it not really worth checking out the early games except to satisfy historical or nostalgic interests.
If I ever manage to beat Wiz 7, I might transfer my characters to 8 and try beating it again. I'm also toying with the idea of starting with 6 and going all the way through, but that would be a truly daunting task.
Also, you don't really miss much story by skipping Wiz 6. The important thing to know is that you find something called the Cosmic Forge, a magic pen that the gods used to write the universe (as your characters know it) into existence.
