If you swore to someone to keep a secret of theirs to yourself, but you broke your word, what are the consequences or religious obligations of this?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

It is not permissible for whoever is entrusted with a secret to reveal it to others. The Prophet said: "If a person says a statement and then turns around (i.e. to assure no one can hear him), then goes away, his statement is a trust." So, revealing a secret is considered as betrayal and this is one characteristic of hypocrites. Indeed the Prophet said: "The signs of a hypocrite are three: Whenever he speaks, he lies; whenever he promises, he breaks his promise; and if he is entrusted, he betrays." [Muslim]

Therefore, whoever has revealed a secret of someone to other people he has to repent to Allaah and be determined not to return to this sin again. However, if one has made an oath not to reveal a secret then broke his promise, he has to expiate for it. For details on this, please refer to Fatwa: 82501.  

Allaah Knows best.