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.
Yamaha U1 Upright, Roland Fantom 7, Roland Jupiter X, Kurzweil Forte 7, Viscount Legend Live, Native Instruments Komplete Kontrol S61 Mk2, Arturia V Collection 7, Komplete 12 Ultimate
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
Acoustic/Electric stringed instruments ranging from 4 to 230 strings, hammered, picked, fingered, slapped, and plucked. Analog and Digital Electronic instruments, reeds, and throat/mouth.
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).