Am no scientist, but First off - the world is not ROUND... its more eliptical ( bulges out equator)..something to do with gravity and motion ( daily spin on axis) and annual around the sun...a hot molten core., cooling exterior (the mantel) - ice caps..etc etc - about 6 years ago
(1) The Moon
Now that humanity knows quite positively that the Moon is not a piece of cheese or a playful god, the phenomena that accompany it (from its monthly cycles to lunar eclipses) are well-explained. It was quite a mystery to the ancient Greeks, though, and in their quest for knowledge, they came up with a few insightful observations that helped humanity figure out the shape of our planet.
(2) Ships and the Horizon
If you’ve been next to a port lately, or just strolled down a beach and stared off vacantly into the horizon, you might have, perhaps, noticed a very interesting phenomenon: approaching ships do not just “appear” out of the horizon (like they should have if the world was flat), but rather emerge from beneath the sea.
(3) Varying Star Constellations
This observation was originally made by Aristotle (384-322 BCE), who declared the Earth was round judging from the different constellations one sees while moving away from the equator.
(4) Shadows and Sticks
If you stick a stick in the [sticky] ground, it will produce a shadow. The shadow moves as time passes (which is the principle for ancient Shadow Clocks). If the world had been flat, then two sticks in different locations would produce the same shadow:
(5) Seeing Farther from Higher
Standing in a flat plateau, you look ahead of you towards the horizon. You strain your eyes, then take out your favorite binoculars and stare through them, as far as your eyes (with the help of the binocular lenses) can see.
Then, you climb up the closest tree – the higher the better, just be careful not to drop those binoculars and break their lenses. You then look again, strain your eyes, stare through the binoculars out to the horizon.
(6) Ride a Plane
If you’ve ever taken a trip out of the country, specifically long-destination trips, you could notice two interesting facts about planes and the Earth:
Planes can travel in a relatively straight line a very long time and not fall off any edges. They can also, theoretically (and some do, though with stops along the way), circle the earth.
Correction (Courtesy of Klaynos, from scienceforums.net): Apparently, planes can circle the Earth without stop about 6 years ago