OMG! I had honestly never head of such a thing until just now. I seriously thought this question was a joke. I was prepared to make jokes involving Pit Bulls or Alligator snapping turtles. Honestly, dogs are the only kind of creatures that I have ever heard of getting stuck together, and that is mostly the result of animals that are a different size attempting to copulate or a problem with the male dog maintaining an erection after ejaculation has occurred.

After further research, a condition known as vaginismus does occur, but it is more common that this condition would prevent sexual intercourse or the penis from entering the vagina, rather than actually "clamping down" on a male while having sex. This has never happened to me before, but these types of involuntary muscle spasms can be very painful. While this is only a recent discovery, it is thought that vaginismus may be more psychological in nature than anything else. That doesn't necessarily mean that the physical symptoms are not real, but this condition is often the result of sever sexual abuse or trauma. The recommended course of treatment is usually psychological counseling as well as education about common sexual myths. Kegel exercises are also recommended to help strengthen the vaginal muscles.

Even with vaginismus, it is highly unlikely that a man and woman will get "stuck together" while having sexual intercourse. (However, if you see this happen, take pictures first, and then pour water on those in the act.)

Vaginismus, sometimes anglicized vaginism is the German name for a condition which affects a woman's ability to engage in any form of vaginal penetration, including sexual intercourse, insertion of tampons, and the penetration involved in gynecological examinations. This is the result of a conditioned reflex of the pubococcygeus muscle, which is sometimes referred to as the "PC muscle". The reflex causes the muscles in the vagina to tense suddenly, which makes any kind of vaginal penetration—including sexual intercourse—painful or impossible.
A vaginismic woman does not consciously control the spasm. The vaginismic reflex can be compared to the response of the eye shutting when an object comes towards it. The severity of vaginismus and the pain during penetration, including sexual penetration, varies from woman to woman.