As far as I know, these are the specific groups that reject (or have at one time rejected) the Trinity as defined in the Nicene Creed:
Jehovah's Witnesses and related (such as the various Bible Students groups)
Christian Scientists (the official Church teaching posits a trinity of the unity of God, the Christ, and divine Science, or: "God the Father-Mother; Christ the spiritual idea of sonship; divine Science or the Holy Comforter" http://en.wikipedia.org/wiki/Christian_Science
Christadelphians (they deny the prehuman existence of Jesus)
Unitarians (they deny the prehuman existence of Jesus)
Mormons (they teach that all humans had a pre-human existance, and that all saved humans will become gods).
Oneness Pentecostals (they teach the Modalist heresy -- that there are three aspects or manifestations of God, not the traditional Trinity which states that there are three Persons that are coequal, coeternal and consubstantial in the Godhead.)
Seventh Day Adventists (in the 1800s) were divided on the subject of the Trinity, but in the 20th Century their church leaders accepted it. Their baptism, however, is not accepted by the Catholic Church because it is not uniformly done "in the name of the Father and of the Son and of the Holy Spirit."
When I was investigating Catholicism, it seemed very telling to me that the only groups that reject the traditional Trinity doctrine are such "fringe" groups. All mainline Christian Churches, from the Catholic and Orthodox through the Reformers and even some of the Restorationists (Church of Christ, for example) teach the Holy Trinity as defined in the Nicene Creed.
Pax,
Ruth