The definition of atheism is "not believing in the existence of god(s)". There is no limitation on spirituality or morals. Indeed, there are atheistic religions. There are numerous schools or Buddhism, some with gods (imported from Hinduism), others without. The original Buddhism does not have gods, and Buddha never considered himself a god either. However, Buddhism is clearly a religion, as it has a structure, rules, temples, etc.
Another interesting case is Shintoism, Japan's "original religion". It is considered by some to be more a gathering of traditions rather than a proper religion, as it lacks rules or a clear aim. Yet, it is organised, has shrines, priests, festivals, etc. Many people will say that Shinto has in fact many gods or deities (called "kami"), but these are not gods by the definition of monotheist or polytheist religions. A kami can be anything... a tree, a stone, a waterfall, a human being that has died... It is better translated as "spirit". Shintoism is recognised as an animist religion, and animism comes from Latin "anima" meaning "spirit". Thus, we could say that Shintoists do not believe in gods but in spirits, and most do really "believe" in them anyway. They can make them up, decide what is a kami and what is not. It is purely spiritual, not divine. In that sense, Shintoism is an atheist religion too.
Another interesting case is Shintoism, Japan's "original religion". It is considered by some to be more a gathering of traditions rather than a proper religion, as it lacks rules or a clear aim. Yet, it is organised, has shrines, priests, festivals, etc. Many people will say that Shinto has in fact many gods or deities (called "kami"), but these are not gods by the definition of monotheist or polytheist religions. A kami can be anything... a tree, a stone, a waterfall, a human being that has died... It is better translated as "spirit". Shintoism is recognised as an animist religion, and animism comes from Latin "anima" meaning "spirit". Thus, we could say that Shintoists do not believe in gods but in spirits, and most do really "believe" in them anyway. They can make them up, decide what is a kami and what is not. It is purely spiritual, not divine. In that sense, Shintoism is an atheist religion too.