Some state prisons do allow these visits, even having special rooms set up for them.
New York and California now even allow conjugal visits between same-sex married partners (religious OR civil unions).
Wiki has a list of rules of all states regarding conjugal visits. Most facilities require certificates that the partners are AIDs or other STDs-free before these "spouses" drop in for connubial visitations.
Leni
I was curious how they handle security for these visits. Couldn’t the incarcerated kill or take hostage the visitor?