No, not dogs in prison but prisons who incorporate dogs as a method of rehabilitating qualified inmates. I love these programs. LOVE. Here's an example.
I cannot tackle the current prison system in the United States. I don't want to, really. I can say that the prison dog program provides inmates with useful job skills, creating opportunities to become working members of society.
More than that, they teach these inmates responsibility, empathy/sympathy, compassion and allow them to form a bond with another living being without any strings attached. The dogs win too, given a chance to stretch their legs, bond with a person and prepare for their new life in a permanent home.
Can you imagine if every single prison in the country implemented this program?
As of 2008, there were 2.3 million prisoners in the United States (the most of any country in the world). 47% were considered non-violent offenders or 1 million inmates. Even if only 20-30% of the nonviolent offenders qualified for this dog program, that would mean 200,000-300,000 fewer dogs potentially euthanized. The recidivism rate of men and women who leave these programs is really low as well.
Courthouse Dogs maintains a great site with a list of programs across the country.