Recently the Eberly College of Science here at Penn State has put together an "Ask a Scientist" program, where anyone can ask a scientific question and it will get relayed to a volunteer with expertise in that area of science. Because I (obviously) signed up and noted that I'm a planet geek, I got forwarded the question in the title. Because I've been lacking for posts recently and this seemed like a good kickoff point for my return, my response was as follows.
Question: Is there any other planets that have an atmosphere. (sic)
In short, yes!
Within our solar system, all of the inner planets except Mercury have atmospheres. But both Venus and Mars have atmospheres that are very different from Earth's and very different from each other's as well. Venus has an atmosphere that is about 90 times heavier than Earth's and mostly made of carbon dioxide. Because of this, Venus has a surface temperature of around 850° Fahrenheit, which is way hotter than we ever get on Earth. Mars is the exact opposite, with a much thinner atmosphere than Earth. Mars probably once had an atmosphere similar to Earth's, but that was about 3.5 billion years ago.
The gas giant planets like Jupiter, Saturn, Uranus, and Neptune all have atmospheres as well, but they're different from Earth because they have no solid surface. All four of them still have weather though. Jupiter in particular has what we call the Great Red Spot. The Great Red Spot is actually like a giant hurricane, big enough that you could fit three Earths inside it. Neptune also used to have a large visible storm in its atmosphere, but it seems to have gone away since our last probes flew by.
Something else you may find cool is that we even know of a moon with an atmosphere in our own solar system! Saturn's moon Titan has an atmosphere just slightly thicker than Earth's, except it's mostly made out of methane. What's really interesting is that Titan also has lakes of methane on its surface and probably even rains methane! On Earth, methane is usually just a gas, but Titan is cold enough that it can easily be either a liquid or a gas, just like water here on Earth.
To take your question even further, we've even seen planets around other stars that have atmospheres! Because the easiest ones to see are the biggest exoplanets, the atmospheres we've seen on exoplanets tend to resemble that of Jupiter so far. Of course, what we're really interested in is finding planets whose atmospheres look a lot more like Earth, and that's probably only a few years into the future.
While, yes, I did give a bit of a simplified answer, I didn't want to write a whole essay on this, and it was targeted at a 4th grader. I should note that there is plenty of other cool stuff out there, even in our own solar system. As I learned while doing some research during my Climate Dynamics course last semester, both Venus and Titan have Hadley cells in their atmospheres, very much like Earth, but also different in a number of respects. I may do a post about Hadley cells in general later on. Just wanted to spark your interest!