The only planets whose atmospheres have been studied are the ones in our solar system. None of them have an atmosphere like ours. The gases in the Earth's atmosphere are strongly affected by the presence of life on the surface of the planet - the huge number of plants which breathe carbon dioxide and exhale oxygen, and the animals which breathe oxygen and exhale carbon dioxide. In addition, planets which are very close to the sun (like mercury) are so hot that their atmosphere evaporates off into space. Mars' atmosphere is more like the Earth's than any other planet's, but a human being could definitely not breathe it.
In the last few years, astronomers have discovered a number of planets orbiting other stars, very far away. They are too far away to tell what their atmosphere is made up of, but if one of these planets were roughly the same size and same distance from it's own star as the Earth is from the sun, it might have a similar atmosphere.

in our solar system Earth is the only planet with a lot of oxygen (21% on earth) in the atmosphere. in fact astronomers will use this fact to search IN OTHER SOLAR SYSTEMS for possible habitable planets. the idea is that since on EARTH we owe our oxygen rich atmosphere to photsynthetic processes , if we can find an oxygen rich atmosphere on another planet it MAY indicate that life is present on that planet as well. so far oxygen in large quantities has not been detected on an extra-solar planet...but the search has just begun so stay tuned!!

To our knowledge, the Earth is the only planet with an atmosphere of the right density and composition to make life possible. Other planets in the Solar System have atmospheres but they are too thick, hot, and acidic like on Venus or too thin and cold like on Mars. The outer gas planets can be considered mostly atmosphere but there is so much (many times the size of the Earth) and it is so turbulent that it can't be compared with Earth. Other bodies in the solar system like Mercury or the Moon have no atmosphere to speak of. The other possibility is that there are planets with atmospheres like ours outside the Solar System. Unfortunately, such a planet would be orbiting a star light years away and we have no technology that could possibly see a planet the size of the Earth at such a huge distance, much less know anything about its atmosphere. Although there is no way to know for certain if there are other planets like ours, we do know that there are other stars that look like the sun out there and these probably formed by similar processes. Do you think such a star could have a planet like the Earth near it?