Grand juries - I've sat on them and had enough friends harassed by them.

The grand jury here in the U.S. is just a tool of the prosecutor. They actually return whatever indictment is asked of them 99.9% of the time. Occasionally a case will be brought before a grand jury if there is political pressure only to have the prosecutor lead the jury not to indict, but normally cases are only brought if indictment is intended and in that case indictments are almost always issued. Virtually no evidence is required to be presented before a grand jury - they will vote indictments consistently with the flimsiest of hearsay. It's a majority vote of the jurors rather than the unanimous verdict required of a criminal trial jury.

That said, the fact that a grand jury is meeting and being presented with a particular case may or may not be secret. The specifics of the proceedings are always secret and sealed as they are occurring, and are frequently the subject of gag orders to force non-disclosure, but potential defendants are frequently aware, co-conspirators may be forced to testify under immunity, lawyers are negotiating with prosecutors, etc.

Plus plenty typically leaks out anyway - corrupt court officers sell information, and so on.