McLEAN, Tex. — No one can remember if the brassiere factory on Kingsley Street here put up barbed wire to keep intruders out. These days, hundreds of strands of barbed wire draw people in.

The old factory building is now home to the Devil’s Rope Museum, a sprawling tribute to the history of barbed wire and fencing tools. It is a wayward cow’s worst nightmare: Bent-corner plate barb, double-plate locked link wire, Bagger’s 1876 barbed single-strand rod and — in the Rare Wire exhibit, protected from the public and overzealous collectors in a glass case — Dodge’s rotating star barb and fixed star on single strand from 1881.

In McLean, a town of about 800 east of Amarillo in the Texas Panhandle, the museum is a bona fide tourist attraction: Anita Seaney, the curator, said it had 6,000 visitors last year....