They seem to have lost some energy. Maybe it is playing a Weber Grill that changes it. 
Muse and the Esbjorn Svensson Trio
The Jam, by some distance
I don’t know if they’re my favorite, but there will always be a place in my heart for the Presidents of the United States of America.
Motorhead post Wurzel.
(No slam against Wurzel, btw. Wurzel was great, but his era of Motorhead = 4 members.)
Honorable mention to the earlier 3pc. incarnations of Motorhead.
Cream
Peter Paul and Mary
Rush
ZZTop
Triumph
Nirvana
The Police
Most of mine have been cited…Hüsker Dü, Violent Femmes, Minutemen, The Jam, Beastie Boys.
I’ll throw the Stray Cats and the Yeah Yeah Yeahs into the mix.
I didn’t know the Jam was a trio. Hmmm, The Jam, Nirvana, or The Police. Tough call. I guess I’ll say Nirvana.
Are we counting bands that were always a three-piece, or including those that did some, but not all, of their best work as a three-piece (like XTC)?
My favorite band for a long time was the trio Ben Folds Five.
To be fair, that is an acoustic session to a very mixed crowd. I wouldn’t have expected stage diving.
Johnny Winter’s first two albums featured him in a trio, not counting brother Edgar sitting in on a couple tracks.
Morphine
Or Genesis, I guess.
I really liked the Fratellis for a few years about a decade and a half ago. Haven’t heard much of their newer stuff though
I’ll add my votes for Beastie Boys and Nirvana.
You may be thinking of this thread from half a year ago about what counts as a “power trio.”
Rush. But then everyone likes Rush. I’m always curious as to what Medeski, Martin and Wood are getting up to as well. The Police put out solid work too, just not enough of it.
The Who weren’t a trio of course, but this clip from the Who’s Next documentary shows how good Pete, John and Moonie were as three-piece outfit.