On a clear day, you can see for miles and miles and miles.
The old saying turns out to be just about true. For a six-foot tall person, the horizon is a little more than 3 miles (5 km) away.
Geometry tells us that the distance of the horizon – i.e. the farthest point the eye can see before Earth curves out beneath our view – depends simply on the height of the observer. For example, if you stood atop Mount Everest (which is 29,029 feet, or 8,848 meters tall), the horizon would be about 230 miles (370 km) away.
Add the effect of refraction, which bends rays of light as they pass through the atmosphere, and the horizon is even farther. Cold weather increases the amount of atmospheric refraction, so in a particularly frosty location such as Antarctica people have been able to see hundreds of miles away.
Plus, since clouds hover above ground level, they can be seen to farther distances than features on Earth's surface.
But just as weather sometimes aids our view, it can also hinder it. Fog and scattered light can limit visibility to below what you could expect based on height. And of course, topography plays a role – even the best viewing conditions aren't much good if there's a big fat mountain in your way (though the view might be pleasing anyway).