Impeachment and expulsion are rarely exercised powers of Congress.
Wikipedia notes that the U.S. House of Representatives has voted to impeach someone just eighteen times in U.S. History. Just seven of those cases (all judges) produced removal based upon a U.S. Senate trial, although five other of the impeached individuals were removed from office after the impeachment by other means (including on Secretary of War who resigned, and not including President Nixon who resigned under threat of impeachment).
In forty-four other cases, impeachment was attempted, but failed to receive a sufficient vote in the U.S. House or were rendered moot before a vote was held, most concern Presidential actions, although Treasury Secretary Andrew Mellon, Supreme Court Justice Abe Fortas and President Richard Nixon all resigned in response to the threat of impeachment hearings.
Fourteen of those cases where an impeached was voted in favor of by the U.S. House involved judges. In four of those cases the judge was acquitted in a trial before the U.S. Senate, three resigned, and seven were removed after U.S. Senate trials. One of the removed judges was later elected to the U.S. House of Representatives.
Two impeachments of U.S. Presidents each produced acquittals after U.S. Senate trials. A U.S. Secretary of War resigned and then was acquitted. A case against a U.S. Senator was dismissed when the U.S. Senate expelled him (which is now seen at the proper process as opposed to impeachment for legislative elected officials).
The impeachment power extends to all federal employees and officers (with the exception of elected legislators), but no one whose position is not subject to U.S. Senate confirmation, other than two U.S. Presidents, have ever been impeached, and no one not subject to U.S. Senate confirmation has ever been removed from office via impeachment.
Expulsion from Congress
Another rarely used Congressional power is the power of a House of Congress to expel its own members. Seventeen members have been expelled (reversed in two cases posthumously) for supporting the Confederacy in the civil war. One was expelled from the Senate for treason in 1797 (he was elected to state office a year later and died of natural causes two years after that). Two were expelled from the House for bribery (among other concerns), both of whom ultimately also endured criminal convictions.
Fourteen Senators were expelled for supporting the Confederacy (in one case a decision posthumously reversed), and one was expel for treason in connection a British and Indian supported insurgency in Spanish Florida in 1797. Sixteen more failed attempts were made to expel U.S. Senators. One Senator's term expired and another Senator died before the process was complete, five resigned, and nine Senators were not expelled because the measure did not receive sufficient support in the Senate (one of the nine resigned shortly after winning the Senate vote). Nine more Senators have been censured (and only one of them won re-election).
Five members of the U.S. House have been expelled, three for supporting the Confederacy (one of which was posthumously reversed) and two for corruption (one was criminally convicted after being expelled for the same acts, the other was criminal convicted before being expelled). At least six members of the U.S. House have resigned under threat of expulsion. At least nine more attempts were made to expel members of the U.S. House were made but not completed (one resigned shortly after the unsuccessful vote, one's term expired before proceedings were complete, one died before proceedings were complete and six were exonerated). At least seven members of the U.S. House have been censured, two of whom then resigned from office.
State and Local Cases
At the state level, at least twelve Governors have faced impeachments by state legislative bodies, with two acquitted, one "suspended from office" without a trial of the impeachment, and the others removed. Another Governor avoided an impeachment by just a single vote in a state house. Some lesser state officials have also been impeached. Many states permit judges to be removed from office by means in addition to or other than impeachment.
One of the first cases I worked on, when I was still a summer associate not yet admitted to the bar, was an effort to expel a member of a city council (it failed).