Listening again recently to King Crimson’s “Lark’s Tongues in Aspic Pt. II” made me realise that this has to be my favourite instrumental number, and figured why not fire up a quickie thread on this.
And that’s - just one, and not one from each of those four categories.
If it’s a different category, like classical, or any other type, that’s cool too.
(Ugh, there is also “Fracture”, off Starless and Bible Black…) 
With a nod to Metallica’s “Orion” as my number two, my favorite instrumental number ever is without question “Charlie’s Blues” by Charlie Byrd accompanied by a drummer and bassist. Live recording. The guitar is all coming out of him, somehow.
Classical Gas - Mason Williams (1968) - Originally named “Classical Gasoline,” the tune was envisioned to be “fuel” for the classical guitar repertoire. The title was later inadvertently shortened by a music copyist. Mike Post, later famous for television theme music, was a producer and arranger for the song.
“Take Five,” by the Dave Brubeck Quartet.
And, “Fire on High,” by Electric Light Orchestra. Though, there are some choral voices at the end of the song, singing the name of the song, so purists might argue that it isn’t technically an instrumental.
For classic rock, nothing beats “Frankenstein” by the Edgar Winter Group, but lately, I’ve been leaning towards a newer track, “Miasma” by Ghost, which honestly sounds like something right out of Winter’s wheelhouse (especially the sax solo near the end).
For the last few weeks I have listened to one, or both, of these two works by Max Richter several times a day.
On the Nature of Daylight has featured in at least 4 movies that I have seen White Boy Rick, Arrival, Jiro Dreams of Sushi and Stranger Than Fiction.
And who would think, “I may just rewrite Vivaldi a little bit.”
Since OP allows for other genres, how about a little twentieth-century chamber music. Gorecki’s second string quartet, second movement.
Well, if it can’t be an entire album, I’ll pick Sorceress from Return to Forever’s album Romantic Warrior. Love this band.
A favorite of mine for almost 30 years is an obscure B side from a Frank Black single.
Saltarello - the Dead Can Dance version. It is quite possibly my favourite piece of music overall.
Oscillate Wildly by The Smiths would be No. 2:
That reminded me - Cecilia Ann is a close third.
can I mention dick Dale’s entire oeuvre?
Otis by The Durutti Column is right up there for me, If we allow a few sampled phrases.
I love Brian Eno’s work as well. His “Apollo” album is excellent and this always manages to calm the storm inside.
Whammer Jammer. The song that launched a thousand blues harp players.
Good choice. I was going to suggest something Brubek. In general I listen to a lot more rock than jazz, but when it comes to instrumentals I can’t think of a rock instrumental as good as the best jazz instrumentals.
I’ll offer up Coltrane’s long version of 'My Favorite Things". Love how he takes the base melody, goes off on tangents, and eventually slides back into the melody. Even though the lyrical version of the song is associated with Christmas, I always get the feeling of a cool, rainy day in Spring or Fall when I listen to this:
For me it’s Coltrane’s “Naima”, one of the most beautiful tunes ever written.
Another is “Soul Serenade” by King Curtis. It was more of a pop tune, I guess.
For rock, it would be “Jessica” by the Allman Brothers.
Another excellent choice.
This one, in the rock department. Though I suppose you could call it soul/jazz:
Camel - “Dunkirk”
