Ghostbusters - Over the years we've heard so much about the plans Ghostbusters 3. Since 1997 alone, I've heard everything from "we're rewriting for a younger cast" to "Bill hasn't signed on for it". If they cant get a third film with the original cast going, then don't reboot it. This was a film that was just the right combination of the right actors, the right director and all the stars aligning.
Back to the Future - The original trilogy is so perfectly done, and is a product of its time. A mix of the actors, the direction, writing and of course the music. A classic like this should never be touched. Plus what car today could possibly rival the DeLorean's coolness?
Taxi Driver- While the story of a distressed war veteran could be easily adapted to work today, the world in which the film took place was a integral part of the story. The world has changed since then so there's no way the film could be remade and stay relevant.
Clueless- A smartly written satire on the rich lives of Beverly Hills teenagers. A great look back at the mid 90's that really couldn't be remade and done justice in my eyes. Great casting and writing make this a film which can be viewed now, or in 20 years and still be funny.
There are tons of other films that shouldn't be remade, I only gave a handful of my choices for this list. Have any suggestions or disagree with my picks? let me know!