We absolutely have, and they are super fun! A first point of clarification, though - there’s no “dark side” of the Moon.
There’s a far side which is never visible from our perspective on the Earth, but with the exception of during a full moon, the far side of the moon is at least partially illuminated. Any portion of the side facing us which isn’t lit by the Sun means that a corresponding fraction of the far side is brightly lit. During a New Moon, therefore, when the hemisphere of the moon which faces us is dark, the entire far side of the Moon is illuminated by the Sun. Ultimately, the far side of the moon is bright for exactly the same length of time as the near side!
Because the far side of the moon is perpetually hidden from us here on Earth, its features are not nearly as familiar to us as the features of the side facing us, visible to anyone who looks up at the sky. On top of that intrinsic lack of familiarity, the far side of the moon is also a very different place than the near side is; it’s almost entirely missing the smooth(ish) dark mare which make up the most obvious landmarks on the near side. The far side instead is almost entirely craters; craters piled within other craters, jumbled on top of each other in a chaotic, rough terrain.
These images are also relatively new to us. We didn’t know how different the far side would be until spacecraft with cameras had been sent to go examine the other half of the Moon. The first images from the far side of the moon came from the USSR spacecraft Luna 3, in 1959. It’s been less than 60 years since those first photos were returned to Earth. By current standards, they’re rather poor images, but they were good enough to tell us that the far side of the Moon was nothing like the near side.
We got another stack of images of the lunar far side shortly afterwards, during the Apollo era. During the Apollo missions, one of the three crew members stayed in the orbiting capsule which would return all three of them home, while the other two journeyed down to the lunar surface. The astronauts who stayed in these capsules instead got a tour of the far side of the Moon, and took a number of photos of the surface from orbit. One such is at the top of the page, taken by Michael Collins.
Nowadays, we have a lot more spacecraft with very impressive cameras aboard, and they send back very detailed pictures of all sides of the Moon. One of these is NOAA's Deep Space Climate Observatory (DSCOVR) satellite which hosts the Earth Polychromatic Imaging Camera (EPIC) for NASA. DSCOVR orbits the Sun slightly on a smaller orbit than the Earths’, at a stable point called L1. This allows the satellite to stay pointed at the Earth, but also to keep a good perspective. DSCOVR therefore sits about a million miles away from the Earth, many times farther than the orbit of the Moon. Every so often, the Moon will cross in front of the Earth, relative to DSCOVR, and EPIC can grab a series of images (which we can turn into a video) of the lunar far side, fully illuminated by the Sun.