The large majority of rebloomers are bearded iris, though some Siberian, Japanese, and other species offer this trait.
Below are some of the most reliable reblooming bearded iris. Note: the time of bloom refers to the first flowering.
Variety, first bloom, height, predominant color(s)
'Autumn Bugler', early, tall (28 inches), purple 'Autumn Tryst', early to midseason, tall (34 inches), violet and white 'Baby Blessed', very early, dwarf (10 inches), light yellow 'Bountiful Harvest', early, tall (33 inches), violet and white 'Clarence', midseason, tall (35 inches), white and violet 'Corn Harvest', early to midseason, tall (30 inches), yellow 'Harvest of Memories', midseason, tall (40 inches), yellow 'Immortality', midseason, tall (30 inches), white 'Jennifer Rebecca', midseason, tall (34 inches), rose pink 'Sugar Blues', mid to late, tall (36 inches), blue