The blue "sphere" represents earth.
The radius of the black circle represents the distance you(out your window or as far out in the ocean, it hardly makes a difference) can see in all directions. But of course In comparison to the size of the earth this circle or ring in reality would be much much smaller so use your imagination to see that the circle would be extremely small on the sphere(earth) in this image. I wanted to make sure you could understand what I meant so I made the size of the circle a bit more comfortably visible.
So, in that little circle on the sphere it is such a small part of the sphere that it is hard to tell if there is any curve to the sphere at all. Especially If you are not near water It would be impossible to tell with there always being a slight change in elevation with land. So being at a beach would make more sense because water has a less dramatic change in it's highth. Still the horizon is flat and all the water seems flat. This is still because of you only being able to see such a small location of the earth that you cannot possibly tell that it is a sphere from the ground.
In conclusion "looking out your window" or actually look as far as you possibly can from on top of the tallest building or at the beach, This would not be relevant to if the world is flat or round. Because it proves both. What it does tell us is that we only see so much because of us being so small compared to the earth.
Adding to this guy's argument, I found some pictures for you FE'ers to try to explain.
(It's from a plane)
How do you explain the clouds appearing to be curved when simple weather dynamics and condensation laws tell you that all clouds in a single cloud bank are at the same altitude? Unless there is some kind of 'bubble' in lower air masses forcing these cloud banks upwards in a bulge (every time this phenomena is observed), these clouds are flying at the same altitude over a curved Earth!
This is near as high as you are going to get outside of an airplane, the top deck of the CN tower in Toronto, Canada. It isn't quite high enough for the curvature of the Earth to be glaringly obvious, but if you look closer you can see the horizon dropping off to the left and right. Open the image in a graphics program and check the location of the pixels, the center of the horizon is higher then the edges.
I guess somebody painted this?
http://lasp.colorado.edu/rocket/Rocket_Movie_4flat.movThis is a link to a video of a rocket reentering the atmosphere - from the rocket. It spins around a lot, I know, but if you slow down the video or pause it you can CLEARLY see the Earth curving and make out the Persian Gulf getting closer.
Another photo from a plane, the Earth's curve is visible.
Unless you guys are suggesting that there is some king of massive conspiracy involving anybody who ever traveled on an aircraft, a very large group of extremely talented artists, and every government that ever spent money on space travel/exploration (they are posting images and movies of a round Earth)), the visual evidence here is pretty much incontrovertible.