Now that we have access to space, the easiest way to prove the Earth is spherical is to leave it and view it from a distance. Astronauts and space probes have done just that. Every picture of Earth ever taken shows only a circular shape, and the only geometric solid which looks like a circle from any direction is a sphere.
2: There is a Horizon
Perhaps the strongest proof of a round earth is that if you stand on any location on the world on a clear day where visibility is not obstructed, you cannot see infinitely in any direction you look suggesting a slow curvature. If you don't believe this stand at the port of a harbor and slowly watch a ship leaving in the opposite direction with some binoculars. You will observe that the ship slowly 'sinks' behind the horizon line.
3: Possible to Circumnavigate the Globe
Presumably with a flat earth, if you travelled so far in for example an aeroplane, one would fall off the edge. Again, real life shows that this is not the case. In 2005 Steven Fosset circumnavigated the Planet Earth without stopping in his aeroplane[1]. After a 76 hour and 45 minute flight, travelling 26,389.3 miles he landed in the area he took off.
[1] http://news.bbc.co.uk...
4: The Existence of Timezones
If the time is 5:00PM in London, it will be 6:00PM in Spain, 1:00PM in New York and a variety of different times across the world.
This can only be explained if the world is round, and rotating around its own axis. At a certain point when the sun is shining on one part of the Earth, the opposite side is dark, and vise versa. That allows for time differences and timezones, specifically ones that are larger than 12 hours.
Another point concerning timezones, the sun and flat/spherical Earth: If the sun was a “spotlight” (very directionally located so that light only shines on a specific location) and the world was flat, we would have seen the sun even if it didn’t shine on top of us. The same way you can see the light coming out of a