Because the doctrine is a construction rather than a single proof-text, it has always had internal dissenters, and they cluster around a small number of rejected options.
Modalism (also called Sabellianism, after Sabellius) held that Father, Son and Spirit are three modes or phases of one person rather than three distinct persons; it was condemned as failing to take the distinctions seriously. Subordinationism, of which Arianism was the sharpest form, made the Son and Spirit lesser; it was condemned as failing to take the unity of Godhead seriously. The developed doctrine steers between the two.
Rejection of the doctrine as such has recurred: the anti-Trinitarians of the Radical Reformation, the later Socinians and Unitarians, and, in the modern period, groups such as the Jehovah's Witnesses and, in a different key, the Latter-day Saints. Each reads the same scriptures and concludes that the councils added to them. The separate quarrel of East and West over the Filioque, whether the Spirit proceeds from the Father alone or from the Father and the Son, is a family dispute among Trinitarians and is treated in its own entry. Across Catholic, Orthodox and mainstream Protestant churches the doctrine is common ground; it is chiefly Christianity's own dissenters who have denied it.