The United States Constitution gives the Senate the power to expel any member by a two-thirds vote. This is separate from the Impeachment power the Senate has over other federal officials. The Supreme Court determined in 1797 that Senators could not be impeached, but only expelled.
Expulsion is an extremely rare event. It has not actually occurred since the Civil War, although this is partly because many members resign rather than face a formal proceeding when expulsion appears possible. Censure, a lesser punishment which represents a formal statement of disapproval, has been more common in the last century. Although censure carries no formal punishment, only one Senator (Benjamin R. Tillman) of the nine to be censured has ever been re-elected.
Expelled Senators
Expulsion proceedings not resulting in expulsion
Many expulsion proceedings have been begun by the Senate that did not lead to expulsion. In most cases the expulsion failed to secure the necessary two-thirds vote; in other cases the Senator in question resigned while proceedings were taking place, presumably because the Senator felt that the proceedings would succeed or that his political career would not survive them regardless. In a few cases the proceedings ended when a Senators died or his term expired.
Censured Senators
Sources
Official Website of the U.S. Senate