I don't know about playing the original Elite with a 3D HMD, but if you don't mind a more modern sort of game, you would appear to have several options. For one, there's an open source Elite remake, somewhat infelicitously called Oolite [1], which could probably be extended to support the Oculus Rift.

There's also something called "Elite: Dangerous", which is a massively multiplayer Elite-style game-to-be, and which appears already to offer Oculus Rift support in its current combat alpha [2].

And, of course, there's Star Citizen [3], helmed by Chris Roberts of Wing Commander fame; in essence, he came to the Internet two years ago and said "Here's what I always wanted to build. How much is it worth to you to play it?" The answer to that question has turned out to be "thirty-eight million dollars and counting", and the full alpha release is projected for late this year, with increasingly large bits of functionality releasing between now and then; I don't know specifically when Oculus Rift support is planned for addition, but I'd be astonished if they weren't looking into adding it.

[1] http://www.oolite.org/

[2] http://massively.joystiq.com/2013/12/23/not-so-massively-eli...

[3] https://robertsspaceindustries.com/about-the-game

(PS: As an old space sim player who's been displeased by the decade-and-more drought of new titles in the genre, I'm delighted to see such a profusion of new titles. Perhaps space railroading time has come around again.)