The most obvious reason is that one can see farther the higher up one goes. If the Earth was flat, any factors restricting your view would not change the higher up you go. However, with a round Earth, the "protruding" Earth would block out far away objects when one is at a low height.
Celestial bodies change positions in the sky depending on where one is on the Earth. Some stars that are visible closer to the equator disappear completely as one travels north. This would not happen in a flat earth.
When there is a lunar eclipse, the shadow of the Earth that appears on the moon is circular, indicating spherical Earth. Although the lunar eclipse happens at the same time for the whole Earth, it happens at different local times, also proving the roundness of Earth.
Circumnavigation of the Earth is possible, and people that circumnavigate experience the gain or loss of a day that other people don't, due to the roundness of Earth.
Finally, we can, have, and do put artificial satellites into space that orbit the Earth, some geostationarily, which would not be possible if the Earth was flat.
I am certain that everyone who reads this blog post believes in a round Earth after reading it. That means it must be infallible.
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