As a rule it is the professional who has the duty of privilege, not the client (In so far as I am aware, a journalists' confidentiality is not a legal protection and I'm aware of cases where the journalist revealing a source was part of the proceedings.).
As such, privilege exists so that the client can reveal very personal information and the recipient is not obligated to testify against them.
In the case of spousal privilege, the protection only holds that the courts cannot subpoena a spouse to testify against you. That said, if your spouse has had enough of your crap, he/she is more than welcome to volunteer to testify against you.
In the case of Lawyers and Doctors, they cannot talk to anyone about your situation unless you authorize them to speak and there will likely have to have it in writing. Depending on the nature of the discussion, the waiver might only authorize certain things.
In the case of a Priest, it is only under specific conditions. While I no doubt believe more than one sect benefits from this, the best known example is The Catholic Church. In the Catholic Church, the privilege only applies to clergy who hear confession (not sure of the exact rules of which rank of Clergy can hear confession, but I know Deacons, which are a lower rank, can hear confessions as well.). This stems from an obligation imposed on them by the Church and a priest that violates this can be excommunicated for breaking confidence. In the U.S., because the government cannot force someone to violate their religion, the privilege is codified in a higher degree of law through the Constitution rather than a statute. Additionally, the priest will likely be the profession most likely to try and get the client to talk to proper authorities about the sin. If the sin in question is a violation of the law, especially a serious one, a priest can include a requirement to confess to the local police as part of the confessor's penance in addition to "Say X Our Fathers and Y Hail Mary's."
In my own community, there was a story I heard where a guy who confessed to murder to the police informed them that his confession was motivated as part of his penance, naming a priest at the church I was going to at the time. When the police reach out to the priest to get his statement, he politely informed them that just because the suspect named the priest as the person who gave him penance, the priest could not discuss what was said to him during the sacrament and refused to even collaborate that he he knew the suspect.
