The first edition of Ender's Game, published by Tor Books in 1985, featured cover art by British artist John Harris, one of the best known Sci-Fi concept artists. This is the image most strongly associated with the book as Tor kept it alive through decades of hardcovers, paperbacks and reprints. However, this artwork has actually nothing to do with Ender's Game as it was originally created for a 1982 re-release of Frederik Pohl's classic SF novel Drunkard's Walk, which is also the title of Harris's image.
Subsequent editions of Ender's Game feature artwork from other famous science fiction artists. The cover for the original German release was designed by Tim White, whose art is all over the place since the 1970s, not just on hundreds of book covers. Several works have been published with collections of his Sci-Fi and Fantasy images, you might recognize some of them from Robert Heinlein or Terry Pratchett books.
Ender's War, a 1986 book release that features both Ender's Game and Speaker for the Dead, sports a cover designed by Vincent Di Fate, another well-known artist and Hugo Award winner. Di Fate was commissioned by NASA in 1985 to create the official painting of the International Space Station.
Both these covers are from Tor Books' Starscape edition, a series that was created to make Tor's back catalogue more attractive to a younger audience. Personally, I think it's more targeted at parents buying "appropriate" books for their children, so it's not a very good idea and doesn't do the book justice. Especially the first release with cover art by a widely unknown artist named David Gaadt -- interestingly enough a Greensboro, SC resident like Orson Scott Card -- makes Ender's Game look like a story for children. Fun times in zero gravity with a cool and shiny suit and helmet.
Tor Books eventually realized that and commissioned Welsh artist Gordon Crabb to give the Starscape cover a facelift. The result is a big improvement over the previous edition, portraying Ender in a typical scene from the book and showing enough of the dark side without focusing on emotions.