There is also a generic instance where the Fifth Amendment privilege doesn't apply--if you're offered "immunity to testify." This is a time-honored technique to use "little fish" to trap "big fish."
Let's say I'm a bank robber and I hired you to drive the getaway car. You drove me to the bank, I went in, and in the process, I killed someone. You drove us away. The cops grabbed both of us. Technically, you can be charged with murder, same as me, because you were an "accessory." But the cops need you to testify against me. So the prosecutor offers you "immunity to testify": If you agree to waive your Fifth Amendment privilege and answer every question truthfully (including admitting that you drove the getaway car and knew it was gonna be a bank robbery) you won't be prosecuted for that crime. If you refuse, the judge in the case can send you to jail for contempt of court.
How is this possible? Because the Fifth Amendment protects you against "self incrimination." But since the prosecutor said you wouldn't face any charges if you admitted what you did, you are, technically, not incriminating yourself.
This is how Paul Castellano cemented his rise in the Mafia. He was arrested with all those other Mafia guys at the famous Apalachin, NY, conference in '57. The cops jailed him with all the others. They offered him immunity to testify against the others. He refused, and spent over a year in jail for contempt of court. (The charges against all eventually were thrown out; otherwise Castellano could have spent lots more time in jail.)