There have been two official versions of Elite for the PC. An EGA version programmed by Real Time in 1987 and later a VGA version ("Elite Plus") programmed by Chris Sawyer in 1991. Elite - The New Kind is a recent PC implementation of Elite pretty true to the original BBC version.
You may find that PC Elite Plus runs too fast on modern PCs, in which case you should slow down your machine with a utillity such as David Keil's AT-SLOW4 (if so, use the command AT-SLOW /C33 /Z) or Ansis Berzin's Bremze.
Click here to download PC Elite (49 Kbytes)
Click here to download PC Elite Plus (240 Kbytes)
Ensure you PKUNZIP with the -d option and that the executable is launched from within its directory.
George Hooper has prepared some
excellent guides and cheats
for PC Elite Plus.