Whether or not you see George Lucas' tinkering with the original Star Wars trilogy as harmless meddling or the greatest sin committed in cinematic history, it's a shame that fans don't even have the choice to purchase HD versions of the original theatrical cuts. But now, at least, a restored version of the first Star Wars is available online. This isn't a "despecialised edition" like many other fan attempts to revert Lucas' changes. Somehow, a group of fans dubbing themselves Team Negative One found an original 35mm film print of the first Star Wars movie, and have spent years cleaning it up, scanning each frame of film and digitally restoring it to make the cleanest version of the original movie as possible. You can check out a video comparing the state of the original film reel and the final, cleaned version below:
Team Negative One's restoration is meant to be more faithful than the only publicly released HD version of the theatrical cuts made available as DVD bonuses in a 2006 release of the original trilogy (which themselves were taken from the Laserdisc release of the movies and suffered from detail loss in the transfer process). It's by no means a perfect restoration, with some graininess and colour differences, and you won't get the sharp image of the Blu-ray releases, changes and all, but it's the closest there's ever been to a true restoration of the original Star Wars.
Due to the highly dubious legality of releasing the restoration, Negative One has remained relatively quiet about putting the restored film online; it began seeding its way through the internet about a month ago, but it's only just started receiving wider attention as more and more fans discover it. Obviously because of this, we can't directly link to where to download the restoration, but should you desire to see it, it's not exactly difficult to find if you go looking.
You can check out the link below to see more comparisons between the restoration and the original print, as well as the 2011 Blu-ray release of the film.