(I apologize if this has been asked before. But I didn’t know what search terms to use.)
So are there any acclaimed musicians who can’t read a note of music?
Depends on your definition of “acclaimed” (as well as “musician”) but I saw an interview with Lionel Richie many, many years ago where he admitted that he’s never learned to read or write music.
I seem to recall Sting saying something similar, but could be way off base on that.
Paul McCartney doesn’t read music. Don’t know if he qualifies as a musician, in the sense that his fame is not based on his virtuosity with his instrument.
Legend has it that Luciano Pavarotti doesn’t read music either, but learns his roles from recordings.
I don’t believe it of any examples you’ll see here. Reading music is just too obvious and too easy.
Bix Beiderbecke never learned to read music, giving him no end of trouble joining the musician’s union to get jobs with bands.
Stevie Wonder?
Most pop musicians (if that’s what the OP is asking about) are not musically literate; it’s probably easier to ask which ones can read music.
I have always heard that Tori Amos can’t read music but can play by ear.
Doubtful, given that she had a scholarship to Peabody
Depends how far you want to stretch your definition of reading notes of music. If you don’t count something like guitar tablature as music, then there are plenty of musically illiterate musicians out there. I don’t think any guitarist I’ve ever played with was able to read standard music notation at any level suitable for performance. If you include tablature, then pretty much everyone reads music.
Reading music isn’t necessary to become a good musician. It is, of course, an immensely valuable skill that I would encourage every musician to learn.
I was amazed to learn that singer/dancer/actor Danny Kaye couldn’t read music.
Watch – now it’ll turn out that’s another UL.
I heard the same of Bing Crosby. AFAICT, the assertion is not debunked at snopes.
BTW, CalMeacham, is there a punchline missing from your .sig?
Music is written in Braille. The late Evan Hunter’s “Streets of Gold,” a novel about a blind jazz musician, has a sample of it, and a interested narrative about how the character reads it.
This gives a thorough explanation of Braille music (albeit far less interesting than the suggestion you give!)
Nothing you can’t figure out for yourself.
Doubtful; Tori went to a very uppity music “conservatory” for college.
He is famed for his ability as a tunesmith, though, having composed some of the most popular and influential songs in pop history. Serious mucic critics have written about the technical intricacies and nuanced sophistication of McCartney’s melodies, harmonies and arrangements. That makes it all the more iroic that Mccartney usually has no idea what they’re talking about.
Okay, sorry to be so slow. It’s been a while since I’ve seen it, and the names weren’t clicking with me. My immediate inclination would have been to embarrass myself by guessing “The Impressionists.” 
I wish the OP would clarify what “acclaimed” is supposed to mean.
In classical or Jazz circles? Probably very few, if any, can get by without a high degree of musical literacy.
In pop/punk/rock/hip-hop circles, it’s completely reversed. Almost none of the artists can read a note, or some small fraction pick up the ability long after they become famous so they can segue to writing Broadway musicals or whatever. The pop divas do rely on folks who can write and arrange music notation, but those folks aren’t the stars. And going all the way to the Tin Pan Alley days and beyond, songwriters would often collaborate with someone musically trained, so that they could communicate their compositions to performers, who in turn relied on some producer or studio hand to play the music back to them so they could learn the songs.