Duke Ellington. Period. He's the one who first showed that jazz could be taken seriously apart from pop music and he was the guy Gershwin listened to for inspiration not to mention he may have the record for compositions by any American composer...and that's not even enough to be considered a short intro! The Harlem Suite probably takes the cake here, with his swelling blues from the start to the cool swing, and back to the moody blues culminating into a awesome, jazzy, and slow march to the end. Bonus points for having been (at least initially) commissioned by Arturo Toscanini, and being a jazz piece that has been, and is still, played by classical orchestras today.
As if Pharaoh Sanders and John Hicks weren't amazing enough already, they came together and made "You Got to Have Freedom", which is just too amazing for words. The intro alone is a minute straight of John Hicks working wonders, and that's before the vocals kick in.
Gershwin's "Cuban Overture" is ten minutes of pure fiesta. And the ending will make you want to get up and dance.
Most songs by the Puppini Sisters. Not even related in real life, these three ladies are putting the swing sound of 1940s pop music into songs like "Walk Like An Egyptian", "Heart Of Glass", and "Crazy In Love".
Bobby Darin's version of "Mack the Knife". The ending is so badass it hurts.
Ella Fitzgerald did a killer version of "Mack the Knife" on her album Ella in Berlin. She forgets the lyrics halfway through and ad libs new ones: "What's the next chorus to this song now?/This is the one now I don't know." She then pokes fun at her flub: "Now Ella and the fellas/We're making a wreck, what a wreck of Mack the Knife." This doubles as a Funny Moment and an Awesome Moment. The best part? She won a Grammy for it.
Listening to Charles Mingus' "Haitian Fight Song" turns panty-waisted poindexters into switchblade-flicking badasses, and makes plain women gain a cup size and a bad (but sultry) smoking habit. Same with "Better Get It in Your Soul".
John Coltrane. For a while, he had the greatest quartet in jazz: himself, McCoy Tyner on piano, Jimmy Garrison on bass and Elvin Jones on drums. That band had a power and an almost psychic interplay that few, if any, jazz bands have ever matched.
Giant Steps is universally recognized as one of the most difficult songs in jazz to perform.
A Love Supreme, an over-40-minute dedication to higher power that is often called one of the most passionate performances in jazz history.
Coltrane's "My Favorite Things" cover takes a well known song and improvises sheets of sound in a nearly 14 minute masterpiece on the soprano sax with a drum, bass, and piano highlighting and adding to the song.
Charlie Parker's "Charlie Parker with Strings". While some purists hate it for being too "pop" for bebop, you have to admit there is something incredible about his virtuoso bebop improvs being played over a full orchestra. There's something even more incredible about hearing his virtuoso bebop improvs being played with just a five-piece band behind him. Bebop is possibly the most difficult-to-play popular music ever, and Parker, Gillespie, Al Haig, Max Roach et al. made it sound not only easy but fun.
Almost anything by Rahsaan Roland Kirk, but "Pedal Up" is probably his most ridiculous tune, especially his live performance of it on "Bright Moments." It's a 12-minute piece which includes circular breathing (he holds out several notes for minutes on end without stopping to take a breath), 3 saxophones (all played by Kirk simultaneously), and the last 3.5 minutes of it are an elaborate solo played just by Kirk without the backing band involving him droning on one sax, setting up a beat and chord progression with another, and soloing on the third (the end solo even has classical-influence harmonization with two of the saxes at once).
Perfect blend of guitar, sax and rhythm: "Lily Was Here" doesn't need lyrics to be awesome.
Louis Armstrong singing "Bare Necessities" from Disney's The Jungle Book (1967). Prepare to feel warm and fuzzy. And "What a Wonderful World". The perfect song to remind you that, yes, the world is worth living for.
Art Tatum. Blind in both eyes, he taught himself how to play and improvise jazz piano by ear, and became so technically proficient that other pianists regard him with awe to this day; one famous story recalls Fats Waller remarking of him, "God is in the house." Listen to Art Tatum playing "Tiger Rag". Now remind yourself that that's only one person playing all those complicated chords and superhumanly fast runs... and he's improvising it.
"Summertime". Written by George and Ira Gershwin. Performed by Ella Fitzgerald and Louis Armstrong. Sheer perfection.
Ladies and gentlemen, Wynton Marsalis based his third symphony around the history of jazz, aptly subtitled the Jazz Symphony. It's basically a concerto for an entire jazz big band and symphony orchestra.
Miles Davis. Listening to album after album of his is like taking the finest walk through an evolution in jazz. Special mention to the haunting introduction to the title track of Bitches Brew.
There was a thing in jazz during the '50s and '60s were a band would perform at small parties set up by producers, and it would all be recorded as a live album. People showed up and were offered booze to help them enjoy themselves. Two classic albums of this particular variety are Mercy, Mercy, Mercy and Why am I Treated so Bad!, both by Cannonball Adderley and his quintet, with special mention to the title track of the former (their most recognizable hit).
Buddy Rich in general. His performance with the Boston Pops, playing West Side Story, caused John freaking Williamsto nearly drop his baton in awe. There's a reason Neil Peart idolized the man. He did things in a suit that any drummer alive would kill to do at all. He is, arguably, the greatest drummer to have ever lived.
A lesser-known Japanese "death jazz" band called Soil & "Pimp" Sessions, especially if you enjoy the faster-paced stuff by The Seatbelts (of Cowboy Bebop fame). So much energy for six musicians (one of whom has the sole job of yelling at the rest through a megaphone, and even then this is fairly rare). Try "Suffocation","Crush","Mashiroke", or "Storm".
Dave Brubeck:
The utterly magnificent "Take Five". Probably the most recognized piece of jazz music in the world. Sexy, soulful, and sophisticated. Made even more epic in the cover by Pakistan's Sachal Studios Orchestra, which adds a local feel. Brubeck loved it.
Brubeck's "Blue Rondo à la Turk", a song made in punishing 9/8 meter with a 4/4 side meter from the same album mixes Turkish music with modern jazz.
Herb Alpert's "Rise". Unfortunately forever linked to General Hospital's rape of Laura by Luke, but still a thoroughly excellent piece of music.
If you think Chuck Mangione was just that guy who did that disco-jazz tune "Feels So Good", you're in for a shock when you hear "Children of Sanchez". 14 minutes long and not a single second is wasted. After a 3:40 minute flamenco shanty with a powerful vocal performance from Don Potter, the second those drums kick in, you're thrust into a jazz/mariachi/flamenco juggernaut that is at once stupidly catchy, tense and powerful and bombastic. The song serves as the theme to a film of the same name, and while you'd be hard pressed finding someone who remembers said film, you're likely to find someone who knows just how amazing this song is.
"What I Say", by Ray Charles. He had twelve minutes left in a set, so he told his band and backing singers "Listen, I'm going to fool around and y'all just follow me". They improvised the song on the spot.
, which is just too amazing for words. The intro alone is a minute straight of John Hicks working wonders, and that's before the vocals kick in.