A polytheistic religion is one in which more than one deity
(god) is recognized and worshiped, such as Hinduism and
Paganism.
The best examples would be the ancient religions followed by the
Babylonians, Egyptians, Romans, Etc. Today there are numerous
people in the world who follow folk religions, pagan traditions and
practice animism. Another good example would the religion of some
of the "Kalash People" of North-West Pakistan. These people are
descendants of Alexander the Great's army and amazingly, they
follow the same religion that people of ancient Greece
followed!
A lot of people would agree that Hinduism is polytheistic.
However this can be debated. Some scholars within Hinduism argue
that the multiple gods and goddesses that are worshiped by Hindus
are actually different representations/incarnations of a single
god. Hence Hinduism can be argued to be polytheistic or
monotheistic depending on which way you look at it.