An epidemic of get-rich-quick schemes is spreading across the country, sped along by Internet technology. Many of these schemes, called "gifting clubs," are cloaked in religious language, claim to have a charitable purpose, and frequently target churchgoers.

Local police, county prosecutors, and state attorneys general have been working feverishly to stamp out the clubs. But as soon as one collapses, others seem to spring up. Nearly all of them are pyramid schemes, illegal investment scams that inevitably collapse when the supply of new members to pay previous ones runs out.

The giving schemes operate under a wide range of names. The World of Giving, a typical pyramid that surfaced several months ago in northeastern Pennsylvania, has four levels: Sowers, Gardeners, Reapers, and Harvesters.

Sowers (newcomers) join a unit of the pyramid, called a board, by paying $2,000 each to a Harvester at the top of the board. Sowers then recruit new members, moving up as they do so, until as Harvesters they hope to collect $16,000 from new Sowers.

The mathematics of recruitment are daunting. After five rounds, it would take tens of thousands of new Sowers to keep a single pyramid going. A Harvester who got in—and out—early enough might reap in excess of $100,000. Most pyramid schemes operate a few weeks or months before failing. The leaders may move on long before prosecutors learn of the scheme.

While some programs are conducted in homes or by e-mail, others draw large crowds at public meetings, where the atmosphere can resemble a revival.

Early this year, so many people showed up in Tacoma, Washington, for meetings of the Jubilee New Paradigm that organizers rented space in the city's Freighthouse Square for their meetings. Organizer ...