The term “piano trio” in jazz usually refers to a group comprising a pianist, a double bass player and a drummer. The pianist is usually considered the leader of these trios, and trios are usually named after their pianist.
Famous examples include:
Nat King Cole formed a piano-guitar-bass trio in 1937 when he relocated to Los Angeles. This format was also used by Art Tatum, Ahmad Jamal, Vince Guaraldi, and Oscar Peterson. Jamal, Guaraldi, and Peterson all later led trios with the traditional format of piano, bass, and drums.
Another fairly common variant is the organ trio, comprising electric organ (typically a Hammond B-3), drums, and usually electric guitar. The bassist is excluded, and the organist instead plays the bassline with his or her left hand (on a keyboard) or their feet (on the bass pedalboard).
Organists Jimmy Smith and Jack McDuff and guitarist Wes Montgomery are among the musicians who have worked in this format. The original line-up of the Tony Williams Lifetime featured Williams (drums); John McLaughlin (guitar); and Larry Young (organ).
Other jazz trios:
Brad Mehldau Trio is composed of Brad Mehldau Piano, Larry Grenadier Bass and Jeff Ballard Drums.
The Bad Plus is composed of pianist Ethan Iverson, bassist Reid Anderson, and drummer Dave King. The group is known for their original takes on rock classics.
Jazz Trios with less common formats:
In 1948, pianist Herman Blount (later known as Sun Ra) briefly played in a trio with Coleman Hawkins (saxophone) and Stuff Smith (violin), dispensing with a conventional rhythm section. Jimmy Giuffre’s 1958 trio also lacked bass or drums, featuring Giuffre (saxophone and clarinet), Jim Hall (guitar) and Bob Brookmeyer on valve trombone. In 1986, Hall was involved in the Power of Three album; his fellow musicians were Wayne Shorter (saxophones) and Michel Petrucciani (piano). In the 1960s, saxophonist Anthony Braxton led a trio featuring Leroy Jenkins (violin) and Wadada Leo Smith (trumpet).
In 1957, saxophonist Sonny Rollins recorded the album Way Out West with bassist Ray Brown and drummer Shelly Manne. Players who used this piano-less format in the 1960s include Ornette Coleman (with David Izenzon and Charles Moffett); Albert Ayler (with Gary Peacock and Sunny Murray) and Peter Brötzmann (with Peter Kowald and Sven-Ake Johansson).
The free jazz guitarist Derek Bailey played in a number of trios, including Joseph Holbrooke, with drummer Tony Oxley and Gavin Bryars on bass, and Iskra 1903, with Barry Guy (bass) and Paul Rutherford (trombone).
The early-80′s group Codona had a line-up of Don Cherry (trumpet) and two percussionists, Collin Walcott and Nana Vasconcelos.