Growing up in El Paso, Jon Filbert loved collecting autographed Major League Baseball trading cards.

“I really was into it, and I still am,” says Jon, now 43. “My collection is up to about 150,000 cards, but who’s counting?”

Baseball cards aren’t all he collects. 

“I collect cancers, too,” he says.

During the last dozen years, Jon has been diagnosed with thyroid, lung, skin and kidney cancers. “In...