Pagan is a word having a related family of definitions that can lead to confusion when having a discussion involving the word. To start with, there is the Roman origin
Webster 1913 alludes to below. Paganus referred to country dwellers, eventually becoming a pejorative not unlike "redneck" or "hick". Since they were away from the cities, movements that took hold in large cities first (such as early Christianity) would take some time to overtake the area. So, Paganus began to refer to those who followed older religions.
Now we proceed to the sense that Webster 1913 highlights — that of someone who isn't like "us". It is possible to find Pagan used to refer to those who are not of a given Christian sect, those who aren't Christian, those who aren't Jewish or Christian, or those who aren't from the Abrahamic religions, also known as the People of the Book: Judaism, Islam, and Christianity. These meanings refer to the idea that the monotheistic religions from Abraham have the One True Path, and the others do not. These definitions envelop atheism and agnosticism as well as Zoroastrianism, Buddhism, Shinto, Wicca, possibly even Unitarian-Universalism, etc. Of course, in the modern era it's quite possible that the internalized definition of Pagan for many people has tones of savages, hedonism, and perversion.
Finally, we reach the realm of the modern self-defined Pagans and their definitions. Of course, disagreement still exists even here. Some modern self-proclaimed Pagans use the Abrahamic definition. Some others define Paganism as being all non-monotheistic religions, which decidedly gets rid of Zoroaster and his followers. Others like to make the claim that Paganism is equivalent to Wicca, reducing the usefulness of both words. The best modern definition in my mind is that Pagan is an adjective and membership term referring to polytheistic/pantheistic faiths. This envelopes Wicca, Druidism, Asatru, Hinduism, some forms of Buddhism, Shinto, Taoism, and many others. This use of the term generally excludes Satanism and similar faiths.
Some would add the term nature-centered in order to fine-tune it somewhat, which also tends to push out the Asatruars, who favor the similar term Heathen as a rule.
Like any other religious group term, Pagan should be capitalized, and of course has adjectives added to it to help subdivide it, such as Neopagan, Mesopagan, and Paleopagan.