God as unity or trinity

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Muslims, Jews, Jehovah's Witnesses and a small fraction of other nominal Christians are unitarian monotheists. The vast majority of Christians have been and still are Trinitarian monotheists.

Unitarian monotheists hold that there is only one "person" (so to speak), or one basic substance, in God. Some adherents of this position consider Trinitarianism to be a form of polytheism.
Trinitarian monotheists believe in one God that exists as three interdependent persons who share the same substance/essence; the Christian version of this is called the Trinity. The Hindu version Trimurti, differs from Christianity in holding that God has three aspects, though shown as anthropomorphs. Trinitarians hold that the three persons of God have the same purpose, holiness, and sovereignty, and therefore each can be worshipped as God, without violating the idea that there is only truly one God to which worship belongs. The Smarta denomination of Hinduism also hold that belief and believe that worship of any aspect of God is equivalent. Although not a perfect analogy, the other denominations of Hinduism, Shaivism and Vaishnavism would be considered unitarian monotheistic faiths.
Ayyavazhi says Ayya Vaikundar is the unity of Ekam, Narayana and a human. (See:Ayyavazhi Trinity)
Mormons believe that there are three separate divine personages (i.e., beings). One of these personages is a spirit without a body referred to as the "Holy Ghost". The other two personages are beings with perfected or glorified (often called celestial) bodies referred to as Heavenly Father (or less commonly "Elohim") and his son, Jesus Christ. They believe that through the mercy of Jesus Christ and by following their religion's teachings, humans are eligible to become gods (sometimes phrased as "become like Heavenly Father") at some point after death and resurrection; this is also called Exaltation.
Rastafarians believe that Haile Selassie is both God the Father and God the Son, made manifest in human flesh as the reincarnation of Jesus, while the Holy Spirit is seen to dwell within all believers (of Rastafari), and within all people (believed by some).
Hasidic Jews hold that there are ten Sefirot (emanations) of God. Each of these are more distinct than a characteristic, but less distinct than a separate personage.
Monism is the metaphysical position that all is of one essential essence, substance or energy. Monism can be inclusive of other interpretations of God.
Dualism is the idea of two, nearly equal divine entities, one being the good God, and the other being an evil god, or Satan. All beings are under the influence of one side, or the other, if they know it or not. Zoroastrianism is an example of dualism.