Here's a view of the moon you'll never see from Earth. This is a picture taken by astronaut Soichi Noguchi while on-board the International Space Station. The photo demonstrates how the crew's position relative to the Moon and Earth's atmosphere create bizarre illusions where the Moon appears to be squished like a beanbag chair.
When Noguchi snapped this picture back in May of 2010, he was observing the moon through the thickest part of Earth's atmosphere. The squishing effect is the result of the air surrounding the Earth acting like a lens; light from the moon passing through the atmosphere on its way to the ISS is bent, resulting in this pancake effect.
Bad Astronomy's Phil Plait provides the diagram below to help illustrate how the Earth's atmosphere behaves like a lens, and explains some of the other features of the illusion, including why the bottom half of the moon appears redder and smooshier than the top half:
The more air you look through, the more junk (particles, smog, and so on) there is, and this stuff tends to scatter bluer light...In this case, the blue light from the Moon gets scattered away, and only the redder light gets through - that's the same reason the setting Sun can look red. The closer to the Earth's horizon you look, the more air you're looking through, and the redder the Moon looks.
You can see that in the diagram here; the ISS is on the right, the Moon on the left, and the Earth with its atmosphere is in the middle. Light from the bottom of the Moon passes through more air as seen by the ISS, so the effects are greater.
In the picture you can also see ripples at the top of the Moon. That's from different layers in the atmosphere having different temperatures, bending the Moon's light by different amounts.
Moonrises are not uncommon on the ISS (the space station orbits the Earth about once every 90 minutes, meaning astronauts on-board can observe up to 16 moonrises and moonsets each day), so views like this one from the ISS aren't exactly rare; but Plait claims that this photo, in particular, presents the most dramatic example of the effect that he's ever seen.