Like a lot of folks here, I'm allergic to musical "bests." But among the most notable trios should be Medeski, Martin, and Wood. Three guys who have played together for so long, they're like 3 heads on the same body. Don't listen to them anymore, but for a good few years my brain was saturated with MMW. You wanna say a different trio is better? Fine, I got no problem with that.
I can't say "best" because there are too many variables - like time period and style. Plus simply put, music is not a contest.
But these represent a cross section of just a few of my favorites.
Contemporary and State of the Art - Keith Jarrett, Gary Peacock, Jack DeJonette.
Classic -- Wynton Kelly or Sonny Clark with Paul Chambers and Philly Joe Jones.
Modern Classic - Herbie Hancock, Ron Carter, Tony Williams. McCoy Tyner, Reggie Workman/ Jimmy Garrison and Elvin Jones.
Timeless - Bill Evans, Scott LaFaro, Paul Motian...also with the grossly under rated Chuck Israel and Larry Bunker. The middle to late '60s with Eddie Gomez. And the last Trio with Marc Johnson and Joe Labarbera.
Pat Metheny, Jaco Pastorius, Bob Moses (Bright Size Life) Bud Powell, Ray Brown, Buddy Rich Duke Ellington, Max Roach, Charles Mingus Emerson, Lake & Palmer Rush The Police Jimi Hendrix Experience Medeski Martin & Wood Morphine Ben Folds Five Keith Jarret Trio Chick Corea, Miroslav Vitous and Roy Haynes (Now He Sings, Now He Sobs)
I'm also a big fan of 1960s era organ trios when players like Jimmy Smith, Jimmy McGriff, Jack McDuff and Groove Holmes and others would play with guitarists like Kenny Burrell, Wes Montgomery, George Benson, etc. There's too many great organ combos to list individually but I have listened to a lot in this genre.
I just find things like this fun because you get to see the diversity of opinions, maybe learn something you didn't know (like, wow THEY were a trio?), and possibly discover things you hadn't heard before.
Following were the responses from Facebook - keeping in mind that not only are people not all keyboard players, but most aren't musicians, and come from a variety of musical tastes....
Ben Folds Five Blink 182 BTO Cream husker du James Gang Jimi Hendrix Experience Kings X! Motorhead MUSE Nat King Cole Trio Nirvana Oscar Peterson Trio Oysterhead (trio supergroup with Stuart Copeland, Trey Anastasio and Les Claypool) Rush sublime The Band Of Gypsys The Jam the minutemen The Police Triumph Vanilla Fudge violent femmes ZEBRA ZZ Top
Guitar Trio - Al Di Meola, John McLaughlin, Paco De Lucia. The Three Tenors - Plácido Domingo and José Carreras and Luciano Pavarotti. Ahmad Jamal Trio - with Israel Crosby and Vernel Fournier. Classic trio from the 50's
John Abercrombie, Jan Hammer, Jack de Johnette - 1974
John Scofield, Larry Goldings, Jack de Johnette - 2006
Larry Goldings, Peter Bernstein, Bill Stewart
Starting at 3:55 is a great performance of Larry's tune "Molto Molto" from a 2015 concert in Italy. Recent albums are billed as "Goldings Bernstein Stewart" ("Live at Smalls" 2011, "Ramshackle Serenade" 2014, "Toy Tunes" 2018). Earlier albums are billed as the Peter Bernstein Trio ("Earth Tones" 1998) or the Larry Goldings Trio ("Moonbird" 1999, "As One" 2001, "Sweet Science" 2002).
in no order whatsoever, and in keeping with the tenets in the opening post...
Air (Henry Threadgill's band, not the French guys) Husker Du (1st-gen punk rocker here) Tangerine Dream A Tribe Called Red The Twilight Babies ( a local Detroit band from the early '00s) Rush ZZ Top The Jam
...Ekova and Austra would've been on this list for sure, but they always have/had an extra musician(s) for their live work. Could probably say the same about Dire Straits, Massive Attack, and Portishead, too.
I'm sure there are many other greats, esp jazz, it's just I haven't been properly exposed to them. Most singer/guitarist acts fall here, but those are mostly glorified one man shows.
Power trio is my favorite band structure. I'm a bassist/keyboardist who does occasional vocals and other instruments. Three is the magic number for artistic, personality, and functionality balance, provided each brings game without overwhelming ego.
I'm sure there are many other greats, esp jazz, it's just I haven't been properly exposed to them. ...
Try these: - McCoy Tyner - SUPERTRIOS (double album, each half a different piano trio) - Jimmy Smith (pretty much anything, but especially with Kenny Burrell) - Sonny Rollins - WAY OUT WEST (sax/bass/drums) - Thelonious Monk Trio (piano trio) - Duke Ellington - Piano Reflections (piano trio) - Mose Allison - BACK COUNTRY SUITE (piano trio) inc. a song made famous by The Who - Pat Metheny - Pat Metheny Trio Live (electric guitar trio) - Bill Frisell - EAST/WEST (modern electric guitar trio with effects) - ProjeKct Two - SPACE GROOVE (avant-garde electronic trio)