David Stout and Carl Hulse, in the NYT (June 9, 2004):

...Ronald Reagan's will be the 12th state funeral in which the deceased has lain in the Capitol. Besides Lincoln, Kennedy and Johnson, the presidents whose state funerals included lying in state at the Capitol were James A. Garfield, William McKinley, Warren G. Harding, William Howard Taft, Herbert Hoover and Dwight D. Eisenhower.

In addition, Gens. John J. Pershing, in 1948, and Douglas C, MacArthur, in 1964, were given state funerals after lying in the Rotunda. While not automatically eligible, they had the honor of being designated by the president as worthy of one. (Vice presidents, chief justices, cabinet members and other high officials are entitled to "official funerals," which are less elaborate.)

Richard M. Nixon also had a state funeral in 1994, but in Yorba Linda, Calif. Franklin D. Roosevelt and Harry S. Truman could have had state funerals, but instead had simpler rites. Roosevelt's body lay briefly in the East Room of the White House before being taken to the family estate at Hyde Park, N.Y., for burial in 1945; Truman was buried in Independence, Mo., in 1972 after services there. ...

The catafalque first used to support Lincoln's coffin has been used to hold the remains of 25 others in the Rotunda, including unknown soldiers from the world wars, Korea and Vietnam; Vice President Hubert H. Humphrey in 1978; and, most recently, Representative Claude Pepper in 1989, according to the office of the Architect of the Capitol.

The catafalque has also been used to support the coffins of senators and representatives elsewhere in the Capitol. It has also been used five times in the Supreme Court building, to bear the remains of Chief Justice Earl Warren in 1974; Justice Thurgood Marshall in 1993; Chief Justice Warren E. Burger in 1995; Justice William J. Brennan Jr. in 1997; and Justice Harry A. Blackmun in 1999. The catafalque was used once in the Department of Commerce Building, to support the remains of Secretary Ronald H. Brown in 1996.