There are a lot of attempts to save Morrowind from the ravages of time, but while it's not the prettiest, OpenMW somehow seems the most ambitious. It's a complete "engine reimplementation" for the old RPG, replacing what was there before with a modern, cross-platform and open source core. If Skywind is a shallow attempt to replace the body of Morrowind with something new, shiny and gold-plated, then OpenMW is the equivalent project designed to augment the game's withered guts.
A new video outlines the progress of the project as of v.0.28.
As the video shows, the game's not yet fully or even mostly playable. When it is, it'll provide a ton of great benefits to players, including being able to play Morrowind on Linux and OSX, support for widescreen monitors, and better water and shadows. It's open source code also means modders should be able to do more to the guts of the game than they can even with the highly-moddable vanilla Morrowind.
You'll likely have heard of other similar projects already: Morrowind Overhaul 3 is a graphical mod that plies the ailing engine with makeup; Morroblivion is (was?) a project to bring the game to Oblivion's engine; and Skywind is a recent effort to pluck the world of Morrowind and drop it into Skyrim.
It's testament to the game's appeal that people are so desperate to stop it from aging into obscurity. There's precious few attempts to do the same for Oblivion.
Morrowind Overhaul 3 is the only one of any of these that really lets you get on with the business of playing the game, although there's reasons to be interested and follow along with the development of all of them. While Skywind is the most pretty, OpenMW seems the most flexible and, in some ways, feasible.
The OpenMW website has download links, documentation and a forum for those who think they can help out.