Keep in mind that Ultima 7 shipped in 1993 so the graphics are dated and it's going to be a problem to run on today's PCs. I recall it needed its own memory manager? Still great though.
There were 10 Ultima games, Ultima 1-7, Ultima 7 Part 2, Ultima 8 and Ultima 9. Ultima 8 and 9 were the worst of the series, with 9 coming out in 1999 and being very buggy and very slow (graphics wise) even though the graphics were very good. Ultima 9 today would probably play better and still look okay graphics wise. Ultima 7 and Ultima 7 Part 2 were the two best of the series with Ultima 4 and 5 being tied in my opinion for next best.
Ultima X is MMORPG and will be out this year but it has no relationship to the series.
There were also some spin offs. There were the two Ultima Underworld games, which were more dungeon crawlers with first person perspective. The first game was the first to have a continuous first person perspective (not grid based in movement for instance), a few months or a year before Doom came out so you can almost think of it as one of the first FPSs. Arx Fatalis was created as a spiritual successor to Ultima Underworld.
There were also two games based on the Ultima 6 engine, Martian Dreams where you went to Mars at the end of the 1800s (yes strange setting) and another one beginning with Savage where you went back in time.
Ultima predates the Amiga by the way. B) I played the first 6 on the Commodore 64 and Commodore 128.