Trillium is a genus in the family Melanthiaceae, according to the Angiosperm Phylogeny Group (APG) website. Other research, by Susan Farmer and others, has placed it within the family Trilliaceae. Either way, it is a somewhat distinctive genus, known only from North America and eastern Asia.
This site has an interactive key and fact sheets for the genus Trillium for the world. It treats only those plants found growing "in the wild" and not those from cultivation. Please feel free to contact me with any feedback regarding the key and fact sheets.