Idaho may only have been a state since 1890, but it has at least 12 companies that have been in continuous, independent operation for 100 years or more. Here's my list - let me know if you have have others to add.
1861: Haworth Farm, Franklin 6th generation (grain & hay farm)
1865: Joyce Livestock Company, Owyhee County 5th generation (cattle ranch)
1865: Owyhee Avanche, Homedale private (newspaper publisher)
1889: CSHQA, Boise employee-owned (architecture)
1891: Hecla Mining Company, Coeur d'Alene public (silver & precious metals mining)
1894: Tracy General Store, Almo private (retail grocers)
1901: Idaho Candy Company, Boise 2nd generation (Idaho Spuds, Cherry Cocktails, Owyhee Butter Toffee and other candies)
1902: Buck Knives, Post Falls 4th generation (manufacture & sell knives)
1904: D.L. Evans Bancorp, Burley 4th & 5th generations (banking)
1907: The White Horse Saloon, Spirit Lake private (restaurant & hotel)
1911: Chesbro Music Company, Idaho Falls 4th & 5th generations (retail & wholesale instruments)
1918: Idaho Steel, Idaho Falls 2nd generation (manufacture food processing equipment)