As Thrunt wrote, Elite was written by David Braben and Ian Bell in 1984 for the BBC Microcomputer in their spare time while they were both attending Cambridge University.
Other than the original BBC Micro version, Elite has appeared on the following platforms:
Elite spawned two ill-fated sequels which David Braben worked on and Ian Bell disowned, Frontier (Elite II) and Frontier: First Encounters (Elite III, I bought a copy), both published by GameTEK. There is a fourth Elite game rumored to be in the works at David Braben's company, Frontier Developments. Most of these games can now be downloaded for free from the Elite Club (http://www.eliteclub.co.uk/) and a few teams of fans are working on single- and multi-player remakes.
On a more personal note, my first exposure to the wonders of Elite was when I got the first PC version from Firebird around 1989. I wasted a good part of my childhood on that, usually playing as a pirate. My strategy was to sell my laser and a missile, scrape together enough for a fuel scoop then go and "reposess" some cargo. (Also, I'd never have to pay for fuel again thanks to sun-diving)
I didn't come across Elite Plus until about a decade later when a friend of mine and I stayed up all night reverse-engineering the save game format. What I liked most about the revamped version was that it improved the graphics significantly without marring the beauty and simplicity of the original.