Leonard Pelly, a wealthy Englishman, was so obsessed with salmon fishing that each year in the 1880s he would load his private steam yacht with his household and servants and head for the distant coast of Norway.

Mr. Pelly’s entourage was part of a stream of British nobility and landowners who traveled so often to the land of fjords and mountains in pursuit of giant Atlantic salmon that the locals named them the “salmon lords.”

In 1887 Mr. Pelly, then 31, took his passion a step further, buying property on one of Norway’s best salmon fishing rivers, the Tengselven near Egersund on the southeast coast. The next year he built a two-story fishing lodge while purchasing several more properties to extend his fishing rights on the river and a nearby lake.

More than 130 years later, fishing rights are still adding value to well-placed properties, whether on Irish streams, English lakes and rivers, Scottish lochs or other waterways.