Of anything. Could be dance, karaoke, a poetry reading, your kid’s kindergarten program, whatever.
Does busking count?
I’ve seen some great street musicians in Europe. There were two guys in Stuttgart who played Bach’s Toccata and Fugue in D Minor on accordians, and a quartet in Prague who played the Pink Panther Theme with the lead on bassoon. Come to think of it, both groups did the same thing; they took a great piece of music, put it into an arrangement that seems ill-advised (at best), and then kicked ass.
I saw a student production of Guys and Dolls at Harvard University starring Nan Hughes. I’ve seen that show many times before and since, but have never seen a finer performance. I memorized Nan’s name so that I could see what would become of her, and was pleased to learn that she did become a professional singer and got to perform at Carnegie Hall, among other places.
When I was a teenager, my brother and I ushered every night at the community theatre during the run of How To Succeed in Business Without Really Trying. Our mom was playing the female lead, but we weren’t there just to support her—it was an amazing show. The cast was so talented, I expected for years to find that one of them had gone on to Broadway or something. (One guy did become a local radio personality). Lots of the show became family catchphrases. The words “no coffee”, “groundhog”, “been a long day”, etc. when mentioned in our hearing may be met with a burst of song.
I’ve never been able to watch the movie or any other version of the play since then, because I know I saw the real one. 
From ‘Britain’s got talent’ - Susan Boyle.
(Sorry, there’s a short advert first)
Back in high school, I saw a very impressive version of Hamlet at Hofstra College. It was an unusual take – Hamlet was clearly only feigning madness, and that allowed them to make “To be or not to be” as a comic monologue (he could see Polonius was watching, so did the entire thing for his benefit, including messing around with the curtain that Polonius hid behind).
A student production of “Antigone” at American University, back in the spring of 2005. It’s a play about big ideas - the duty of the individual to her conscience versus duty to the state, among others - and about characters who think deeply about them. These guys managed to sell that, and also delivered on the creepy, surreal character that a good production of this play should have. (A Greek chorus is the personification of Fate itself, as I understand it - if it isn’t creepy, it’s being done wrong.)
I saw a high school performance of Kiss Me Kate with a tiny little 17-year old as Kate. She had a REALLY big voice. She later went on to be in a road company of A Chorus Line, a small part in a movie and had a long career in regional Equity theater. I don’t know if she ever tried to break into New York theater, but she definitely had Broadway-level talent.
I saw a production of The Diary of Anne Frank a few years ago at the El Paso Playhouse. The girl playing Anne was ASTOUNDING. I don’t think I’ve ever seen a better performance from anyone under the age of 30.
George Bernard Shaw’s Pygmalion performed by Dramashop at MIT back in the 1970s. Perfect production.
Not completely sure about “best” ever, but very very memorable, in that I saw it 25 years ago and can still “see” some of it…
Back when I was in High School (a boys-only HS) I attended a production of “Twelfth Night” being put on by our sister-school down the road.
Twelfth Night with its cross-dressing and twin brother & sister, and romances of mistaken identity with an all female cast. 
Early Wifey & Hubby videos.
High school performance of Fiddler on the Roof. Kids just absolutely nailed it. One of the girls that plays the daughters, though, was hit and killed by a drunk driver a year or two later. A friend of mine still has a recording but says she can’t watch it.
I had a friend who was a triple threat–could dance, sing, and act.
Unfortunately, she could do none of these in front of a group of people. When auditioning, she would freeze and vomit.
She is now an entertainment lawyer.
Our local high school did some superb versions musicals, including My Fair Lady, Annie Get Your Gun and The King and I.
I understand they did a terrific version of Barnum, too. I can’t imagine that being done in high school (though, I saw the lead actor the next year as Doolittle in My Fair Lady and it was clear he was a strong talent).
Years and years ago, we were at a Chieftains concert (An Irish Evening tour with Nanci Griffiths and Roger Daltrey), and saw a young (16 years old?) dancer named Jean Butler who danced a couple of numbers each night. She was astonishingly talented.
She went on to headline Riverdance.