Mormons are often accused of polytheism, and the accusation is generally meant to exclude them from the respectability of Abrahamic religion (the established monotheism of Christianity, Judaism, and Islam). The notion that the LDS would be excluded from Abraham’s legacy would strike many LDS as bizarre, particularly given the fact that the scripture named for Abraham is a vital text in understanding Smith’s vision of the nature of God’s relationships to humanity and to other beings.
I have often been reminded by reasonably knowledgeable and well-intentioned Latter-day Saints that in point of fact Smith was a henotheist. While I am sympathetic to the underlying impulse (shielding Smith from the opprobrium of the monotheists), that answer is misleading. Henotheism indicates a belief in one’s own, generally national/ethnic, God who exists in a world in which other gods of other nations are also believed to exist but to have separate jurisdictions. The YHWH of the Hebrews, and in fact much of the theology of ancient Mesopotamia, is maintained to be henotheistic in this sense. Elijah’s great success in igniting wet wood is understood to be evidence of YHWH’s great power over competing gods (represented by Baal) rather than the fictitiousness of the competing Gods.
This henotheism was then seen to lead naturally to monotheism as one’s national God was finally realized to be the only true God. The Mormon henotheists argue (at least implicitly) that God’s divine relatives function as distinct “national” deities and thus cannot be considered anything like the “pagan” pantheon depicted by (generally evangelical Christian) critics of Mormonism.
Polytheism, on the other hand, generally is conflated with something like the Greek pantheon, in which some more powerful gods maintain a court in which a variety of other gods live and have their function. Often it is equated with pantheism (which itself has several different forms). Polytheism (or at least kindness or respect toward henotheistic competitors) is decried throughout the Hebrew Bible, and the Christian Bible preaches a single mighty God. Later Christian interpretation has made clear the mystical separation of humans from God (even as the Atonement mediates a reconciliation), even though the central honorific of the Christian Bible for God is Father.
I would submit that Smith actually taught a vision of God’s relationships separate from monotheism, henotheism, and polytheism. For lack of a better neologism, I would prefer familotheism. The more I read Smith’s own writings and preachings, the more convinced I am that he truly did see patriarchal kinship networks as encompassing not just all of humanity, but all of the vast upper expanses of what he and his followers called the “scale of creation.” Working from the Christian Biblical context, he appears to have emphasized above all others the relationships implied by God’s paternal honorific (seen as mighty metaphor for Creation and salvation by mainline Christians). Angels, for many Christians an approximation to polytheism, were for Smith a part of that same kinship network, siblings and cousins in the eternal family tree.
This position will cause problems for systematizers and theologians because it appears to be an explanatory system drawn from outside formal theology and will tend to defy the coherence so coveted by scholastics and their conceptual heirs, but I believe it is both more honest and perhaps more illuminating than characterizing Smith as a henotheist.
 Not enough time for formal footnoting or a more comprehensive treatment, but I will point to the full and formal argument when it is published.
 I am open for disagreement. Was Smith a henotheist? Monotheist? Polytheist?
 I am also interested in amplifications or insights. What does this conceptualization of God imply for Mormon theology and faith culture?
 In terms of interactions with outsiders over this issue, perhaps it could be summarized as “Joseph Smith believed in God as a Father in a much more literal sense than his Christian peers, and though the details are somewhat complex, God’s involvement in the family of which we are a part is central to our worship of God, whom we affirm as our only Divine Father and the exclusive object of our worship.”