Designed by: Richard Garriott (main designer, creator)
Influenced by: Difficult to say. Definitely D&D, but the dungeon exploration mode looks too much like the PLATO/Wizardry system to be accidental, although it's possible the algorithm was independently-derived.
Series: Nine "core" games were made by Origin, but Ultima VII had a couple of large expansions that are by all rights games in themselves, there's a still-extant MMORPG, and there are several other side-games made by them. Japan has a couple more games, the Runes of Virtue sub-series.
Legacy: The Ultima series is the forefather of the vast main category of CRPGs.
Wizardry didn't change much among the majority of its lifespan, but the Ultima games changed greatly during their early years. This article is mostly concerned with the earlier games, but the flow of its design can be traced up as far as Ultima VII, generally regarded as the zenith of the series' popularity and influence.
The first games (technically the first Ultima game was Akalabeth) were dungeon-crawly things, but without the benefit of Wizardry's many specials or mapping tricks. Dungeons were primarily just places with monsters, and the occasional important plot item. They tend to be less interesting places than Wizardry's treacherous dungeons.
That's okay however, for Ultima brought us what has become known as an "overworld," a tile-based world in which the dungeons are set as special locations. It also brought us real towns, and a routine for speaking with people (instead of treating them as another thing to handle with specials).
Later Ultimas would even allow for interactive conversations with characters. This was usually handled using keywords, where speaking with people would reveal some things that could be asked about, either with that character or others.
Ultima IV (Screenshot courtesy http://braid-game.com/)
Another difference between the two is that story is of much more import in Ultima, and ties more deeply into the play mechanics. One result of the difference in focus is that the original Wizardry holds up much better today than the first two Ultimas, whose story was rather slight, and even a bit goofy. Later Ultimas, however, have a world with nearly unequaled depth and complexity. The third installment has a whole hidden continent to explore, Ultima IV brings NPC relations to the true heart of the game in its virtue system and bossless design, and Ultima VII may have the most engaging RPG world ever devised.
Sadly, the last Ultima game was released over a decade ago now, and between Richard Gariott's exile from the company and Electronic Arts' decided lack of interest in their older properties, this state of affairs might never change. Ultima Online continues to cling to life, but the days of it being the MMORPG leader are long over. When it finally goes dark, it'll be the end of the greatest series of CRPGs ever known.
Further reading: Blogging Ultima