Anthony Mancinelli shook out a barber towel and welcomed the next customer to his chair in Fantastic Cuts, a cheery hair salon in a nondescript strip mall, about an hour’s drive north of New York City. “Hey, paisan — same as usual,” said John O’Rourke to Mr. Mancinelli, who began layering Mr. O’Rourke’s hair with his steady, snipping scissors.

“I don’t let anyone else touch my hair,” said Mr. O’Rourke, 56, of Cornwall, N.Y. “The guy’s been cutting hair for a century.” Actually, Mr. O’Rourke was off by three years. Mr. Mancinelli is 107 and still working full time, cutting hair five days a week from noon to 8 p.m. He has been working in barbershops since he was 11. Warren Harding was in the White House.