Rudy Williams (nicknamed Looney; 1919 Newark, New Jersey – 1954 Cape Cod, Massachusetts) was an American jazz alto saxophonist.
Williams started on saxophone at age twelve, and concentrated on alto, though he was also capable on baritone and tenor sax. He became a member of the Savoy Sultans in 1937 and recorded frequently with the group. In the 1940s he played with Hot Lips Page, Luis Russell, Chris Columbus, and John Kirby, and led his own bands in Boston and New York City later in the decade. He played with Tadd Dameron in 1948, and after more time as a bandleader in Boston in the early 1950s he played with Illinois Jacquet and Gene Ammons in California. As a member of Oscar Pettiford's band, he toured East Asia in the 1950s.
Williams also recorded with Howard McGhee, Dud Bascomb, Don Byas, Babs Gonzales, Eddie "Lockjaw" Davis, Eddie Vinson, Bennie Green, and Johnny Hodges. He never recorded as a bandleader. After his death, Charles Mingus wrote a memorial piece, Eulogy for Rudy Williams, then recorded it for Savoy. The liner notes of the Savoy album state Williams died by drowning in summer 1954.