I claim that my speakers have negligible horn coloration, and wouldn't have too much trouble coming up with quotes (including from avowed horn-haters) which support that claim. I also claim to not be the only one by far - among designers that I'm somewhat familiar with, Earl Geddes and Wayne Parham also have designed horn-type speakers that have negligible horn coloration. I follow in Earl's footsteps in using waveguide-style horns.
In general, a good smooth horn profile combined with a good crossover to an appropriate bass section should result in negligible characteristic horn sound. Different designers have different ideas about what the best horn profile is, of course.
In pursuit of soundstage depth, among other things we want a fairly wide, uniform radiation pattern with minimal diffraction (which can give away the speakers as the sound source).
In my experience a good dipole or bipole system does a better job of conveying a sense of instruments in three-dimensional space than a comparable monopole does, and so my best horn systems are bipolars. I'll be showing a rather innovative evolution of the bipolar theme (invented by James Romeyn) at RMAF in a couple of weeks; my room happens to be right next door to the Volti Audio room, Volti being the high-end horn speaker that Art Dudley liked, linked to by devert above.