I'm shocked by 1) the fact that some of you think the only evidence we have for a round earth comes from NASA (they were created in 1958, people! We had plenty of evidence before then, too!) and 2) the fact that relatively few RE'ers have challenged this.
I'm also surprised that nobody has mentioned
seismic waves. When there's an earthquake in New Zealand, the waves can be detected in Spain
in exactly the way you would expect if the Earth were round. There are tons of other phenomena in geology that only make sense with a round earth.
Also, there's the fact that boats and planes do a perfectly fine job navigating the Southern hemisphere, even though all the RE maps of that area should be essentially useless if the earth actually looks like the
azimuthal equidistant projection that people on here seem so fond of.