
The Ultima 6 Project worked closely with Team Lazarus and some Team Elemental, and became the second major Ultima remake (after Lazarus) to reach completion.
Ultima 5 - Lazarus is finally complete, after 5 and a half years of development. It did what the more largely anticipated Ultima 1 - A Legend is Reborn could not - reach the finish line. After releasing two demos in a short span of time in 2004, Lazarus was officially released on 22nd December 2005.
Ultima 2 in Windows is hosted at Ultima: The Reconstruction and can be used to run Ultima 2 under Windows. Unlike the other engines listed here, this does not seem to be cross-platform and focuses only on Windows. The last release dates back to 2000, and the project does not seem to be maintained any more, but that doesn't matter as it is complete after all. Along with the ability to play the old Ultima 2, there are also options you can set to your comfort, such as the screen resolution, the colours and the ability to easily restart the game.
Ultima IV Reborn is another Ultima 4 remake for Neverwinter Nights; very little is known about it at the moment and not many people know about it (it isn't listed in many Ultima sites). Judging by the comments, this remake deserves much better popularity.
David Randall recreated Ultima 5 specifically for TI calculators. I had created a page about his remake to centralise information about it.
See also: the forum thread where this was announced in 2007.