Organ transplants are serious business, which explains why insurance underwriters treat them on a case-by-case basis.

"It really depends," says Goldstein. "Kidney transplants are one of the more common kinds of transplants and we do insure individuals. There are lots of different aspects that we need to look at with someone who has had a kidney transplant, but most of the industry will underwrite those individuals depending on how well they're doing with that transplant. But assuming that they're recovering from their surgery, they're doing very well, they're not having any complications from the transplant, kidney transplants can be underwritten."

How about liver or heart transplants?

"Liver and heart transplants might be insurable by some carriers, but I think it would not be insurable by many," Goldstein says. "There just hasn't been as much experience to be able to know exactly what the risk classification should look like. I would be reluctant to say that nobody is doing that, however."

Bloom says New York Life steers clear of organ transplants, except for some kidney transplants.

Goldstein says at least one category of transplant recipients can look forward to a very favorable risk class: corneal transplants.