My father used to travel on Concorde. When asked about seeing the curvature of the Earth, he thought it was pretty imperceptable, albeit beginning to become noticable, and probably due more to the power of suggestion or camera distortion than anything else. He thought, apparently, you have to go up in the likes of U2 aircraft (70,000 feet) before one really has a spectacular view of the Earth's curvature, although of course the view from Concorde certainly was unique and spectacular. I only flew it once when a child.
It might also be a very subjective thing, "seeing" the curvature of Earth. Technically, one could see this on a beach as a tall ship approaches over the horizon. This would be even more true in the open ocean, where one has an unobstructed view in all directions, when some people I know have claimed to be able to see the curvature. Or as others have said, just before dawn or right after dusk when a thin sliver of light remains. Being above the weather, even in subsonic aircraft, also seems to reinforce the perception of being able to see the Earth's curvature, which certainly was true of Concorde.
But I've never seen any photos from any civilian aircraft as spectacular as some of stuff coming from weather balloons and military aircraft. If commercial space travel ever becomes viable, I would want to do it just to see sights such as those. ^