I have no idea why you'd want a curved door, but I suppose there's always clients who'll want different for the sake of different. If that's an itch they need scratched, an Italian manufacturer called Linvisibile manufacturers curved, hinged doors with a ten-year warranty. These are "distinguished by the use of adjustable concealed hinges," they write, "and the absence of door frames or jambs to achieve seamless continuity between wall and door."
There are of course frames--just invisible ones (i.e. concealed within the surrounding walls) made from extruded aluminum. The doors themselves are hollow-core, hardwood-framed and MDF-skinned, with a honeycomb layer between. And they can be ordered in any permutation of concave/convex, left-hand/right-hand, swing-in or swing-out.
One of the use cases they cite is a London home owned by "a family of sailors" who wanted a nautical, boat-like feel to the interior.
I suppose the aluminum frame goes a long way towards making the installation easier, assuming the walls are plumb, but man I wouldn't want to hang one of these.