Most movie remakes are second-rate exploitative pap produced by the creatively bankrupt, of course. In order to make my list, a movie has to be more (less?) than that. It's not enough to be incompetently executed, preferably on a budget hugely larger than the original, or devoid of redeeming artistic merit. To make this list, a remake has to somehow miss the most essential point of the appeal of the original.
Here we go:
Planet of the Apes: The most memorable and dramatic element of the 1968 original is the moment when Charlton Heston discovers what planet he is really on. Needing a new twist for the 2001 remake, director Tim Burton gave us an ending in which... nobody can figure out what the hell was supposed to have happened. Up next: Burton remakes Soylent Green. Heston has a non-speaking cameo as a dead body.
The Day of the Jackal/The Jackal: The 1973 original was a brilliant psychologically tense thriller in which the ruthlessly efficient assassin and doggedly determined detective converge in a nailbitingly tense finale. The 1997 remake gives us Bruce "One Note" Willis as an assassin whose combination of ludicrously over-complicated plans and incompetent execution makes him the least likely killer this side of Wile E. Coyote.
Deathrace 2000/Deathrace: The makers of the 1975 original took a cast comprising some of the least talented stock players of the day plus a threadbare budget and created a much-underestimated satire on the dehumanizing effects of violence as entertainment. The makers of the 2008 version gave us a forehead-slapping celebration of the same thing. Deathrace is like watching somebody else play a video game.
Rollerball: 1975 original, satire on celebrity culture. 2002 remake, celebration of same. See Deathrace above.
Psycho: The 1960 original retains the power to scare to this day, even for audiences familiar with its central plot twists. Gus Van Sant's shot-for-shot remake replicates every move of the original, even intentionally including many of its continuity errors, yet somehow fails to deliver its tension. With what may well be the cardinal definition of the unnecessary remake, Van Sant proves that it's possible to play all of the notes and none of the music. This is the film-making equivalent of karaoke.
The Day the Earth Stood Still: Yes, I know the remake isn't even out yet, but the casting of Keanu Reeves as the alien Klaatu when his acting skills far better suit him to the role of the robot Gort is enough by itself to get it on this list. Add to that the fact that 1951 original is intractably rooted in the Cold War fear of mutual destruction. Lacking the threat of nuclear warfare as a compelling driver, in the remake the aliens are, reportedly, concerned about mankind's destruction of our own planet's environment. So in his departing speech Klaatu is going to threaten us with... what, exactly? If we continue to destroy our planet, his people will send Gort to... uh... destroy our planet?