Off the top of my head, I can think of Rush, ZZ Top, The Police, Nirvana, Emerson Lake and Palmer, Cream, and a thousand other bands that don’t immediately come to mind.
Of the ones that I can think of, it’s very hard to pick a favorite but I think I’d have to go with “The Police.” They had so many good albums in the 80’s and were on top of the world. Of the groups listed, their songs might still be the most popular.
Who’s yours?
A tossup between The Jam and the Nat Cole Trio.
The Police for me.
Rush is in there somewhere.
The original George Thorogood and the Destroyers was a 3 piece.
The Toy Dolls, Agent Orange, and Material Issue.
Off the top of my head, Cream.
But then I run into the case of Crosby, Stills, and Nash. They were a three person band on their first, perfect, album. Then they added Young and backup musicians for touring. Then Young left and they were the better for it. Backup musicians continued to float in and out and Young came back irregularly.
Most bands use additional musicians at times. Are they still trios? I think we’ve had a thread about that, but I don’t want to dig it up.
Of the bands listed so far, my favorite would be ELP.
A pretty good group not mentioned yet: The Jimi Hendrix Experience
Motorhead was a trio for most of its existence.
The Michel Petrucciani trio.
For me, probably Rush and ZZ Top.
While I wouldn’t necessarily classify them as one of my favorites, the James Gang were a power trio, and I love a couple of their songs (“Walk Away,” “Funk #49”).
Same. Throw in Pink Floyd if we don’t count Roger as a Person. 
Crosby Stills and Nash.
I forgot…
Yeah. CSN should be on the short list for this.
Do be fair, they were four people for a bit (Crosby, Stills, Nash & Young).
Dinosaur Jr.
With runners-up Violent Femmes, Lucie Too, Kælan Mikla and Skating Polly.
I think that I’ll go with Bob Mould and any two people he feels like sharing a stage with. If I had to choose which two people, it would be a spectacularly tough choice between his bandmates in Hüsker Dü, Greg Norton and Grant Hart, and the rhythm section he’s spent the last decade and change with, Jason Narducy and Jon Wurster. (Had Sugar lasted a bit longer, I would throw David Barbe and Malcolm Travis right up there in the mix.)
I did not know they were only three members.
Hell yeah! Definitely on the list (IMO).
I’d take Sugar over Hüsker Dü regardless of how long they lasted.
I think Beastie Boys should be on this list. (just occurred to me)
What do you mean, were? Are, man, are… they still rock. Check out that “drum kit”:https://www.youtube.com/watch?v=ICixXOKmYbQ
Although, I have to say, Gano is looking a lot like Brad Dourif-as-Wormtongue…