I've always been slightly enamored with the rotary drop doors that slide under the car [1]. I would never buy a car with them, but they are interesting none the less.
The problem with these doors is the complexity and the fact that a simple tree branch stuck in it would completely fuck it up. The complexity means that it will break much more often than a regular door - it has motors and multiple pieces.
Also imagine a child sticking a finger in it while it's closing, turning it into a meat grinder.
[1] http://www.youtube.com/watch?v=AAtkoje4-eM&t=35s