"Jazz is the type of music that can absorb so many things and still be jazz."
"Jazz is freedom. You think about that."
OK, OK, that probably didn't help much, but in our defense, defining jazz really is hard (just look at what the Other Wikihas to say about that!). So maybe we can just stick with the following: At its heart, jazz is about spontaneity. That usually means improvising, the art of playing (to a greater or lesser extent) without a script and being free to play whatever you like, sometimes without even confines of traditional music structure (which is what Free Jazz is all about).
Jazz started out in the United States in the beginning of the 20th century as 'black music' and is closely related to Blues, to the extent that many famous jazz compositions can be considered Blues pieces. Since then, there have been different forms of jazz, listed roughly in historical order: New Orleans, Swing/Big Band, Bebop, Cool, Modal, Free Jazz, Fusion, Nu Jazz... and this is a very incomplete list.
Jazz itself probably started out in a small band format in many different cities throughout the US, most famously New Orleans. It became the most popular type of music in the US in its Big Band format (10-30 musicians) during the Twenties to Forties. Then it evolved into a multitude of different styles, pretty much all of which were played by small bands (duos to octets), starting out with Bebop. The emphasis also changed back to playing more in jazz clubs and having fewer concerts (with some important exceptions, such as the Newport Jazz Festival). The ascension of pop music and Rock & Roll in The Fifties led to the fading of jazz's popularity. Jazz today has, for the most part, a sizable but 'cult' following. Somewhat amusingly (and probably shockingly to the original founders of the genre), jazz has become "respectable" music thanks to the development of technical artistry; jazz is now taught alongside Classical Music in many university music departments across the US—unheard-of for any other genre.
Jazz has left a deep impression in music. Improvised and/or extended solos are the primary example of this. Jazz also contributed to the development of musical instruments, most famously the modern drum set, which was largely developed by early jazz musicians.
Jazz is one of the most unique cultural contributions that the United States brought to the world, along with Rock & Roll.
Finally, a note on the name: there are many, many, many ideas for where and how the word originated.
Notable jazz artists include (note, some of these musicians belong in multiple categories!):
Big Band Era
"Jelly Roll" Morton: New Orleans-style jazz pianist and the genre's first great composer. Also an inveterate braggart who claimed to have single-handedly invented jazz and a Boomerang Bigot who frequently insulted darker-skinned musicians while emphasizing the white portion of his mixed-race heritage.
Buddy Bolden: New Orleans cornet player, often regarded as one of the most important pioneers of jazz, but whose reputation is based entirely on verbal testimony because he never got to record anything: he suffered a psychotic breakdown in 1907 and spent the rest of his life in a mental institution, and the first jazz recordings weren't made until ten years later.
Dominic "Nick" LaRocca: A highly controversial figure in jazz history, cornet player LaRocca was the leader of the Original Dixieland Jass Band. He's probably the first jazz musician who was ever recorded, and the first to outsell John Philip Sousa, who had the best-selling artist in America at the beginning of the twentieth century. At the same time, he was notorious for claiming that jazz was exclusively an invention of white musicians and trying to bribe other trumpeters to leave New Orleans so he could be the best in the city.
Paul Whiteman: Known as the "King of Jazz", Whiteman was one of the first white bandleaders and helped to bring jazz to mainstream attention. Having been trained as a classical violinist, he received some criticism from other classical musicians for "playing below himself", while some black musicians felt he was becoming famous by copying their style. Nonetheless, he helped to introduce the style to white audiences and did his best to give credit to black musicians whenever he could.
Louis Armstrong: A massively influential jazz musician, played the trumpet and cornet, and engaged in a fifty-year career in jazz. He is considered the Trope Maker or Trope Codifier for many basic elements of jazz, including scat singing but chiefly improvisation: he's the first great jazz soloist to have been recorded. His later records aren't really jazz but are still highly enjoyable; his recordings from the late 1920s, made when he was already a veteran musician in his own late twenties, are essential listening.
Duke Ellington: The greatest composer and bandleader in jazz, although he claimed to dislike the J-word and preferred to have his music described as "music". His outstanding compositions notwithstanding, he was perhaps even greater as a bandleader in that he encouraged others (such as Billy Strayhorn) to write classic compositions for his band, and fostered more than one generation of great players (Jimmy Blanton, Ben Webster, Johnny Hodges, Paul Gonsalves). Also a damn fine pianist, and possibly the only jazz musician who could have been equally at ease playing with both Louis Armstrong and John Coltrane, although not on the same date, alas. Miles Davis, his only rival for the post of Greatest Bandleader Ever, said that jazz musicians should get down on their knees every day and thank Duke for what he did for music.
Count Basie: Jazz composer and bandleader (and pianist as well) at the same time as Ellington, Basie's unique styles mark him solidly as a quintessential Big Band leader, along with Ellington. Developing his style with a number of orchestras, Basie specialised in riff-based jazz, which is Exactly What It Says on the Tin.
Benny Goodman: A classically trained clarinet player known as the "King of Swing", Goodman was responsible for helping to bring hot swing which focused on improvisation into the mainstream in the 1930s, and made an effort to employ black musicians at a time when the music industry was segregated.
Fats Waller: Fine pianist and singer but chiefly memorable for writing great songs, some of which ("Honeysuckle Rose", "Ain't Misbehavin'") are so standard it's almost ridiculous.
Art Tatum: An almost completely blind jazz pianist, whose technique is something that, that, ... Just see for yourself. No wonder too, as (so legend goes) he learned to play by repeating the movements on a autopiano... which played pieces for four hands! Playing his material is a truly monumental achievement even to this day.
Chano Pozo: A short-lived but highly influential Afro-Cuban percussionist best known for his work in Dizzy Gillespie's various outfits, where he played a crucial role in the establishment of Latin jazz. A heavy drinker and brawler, he was shot dead at the age of 33; while there are multiple stories about why he was killed, the prevailing one is that he threatened a marijuana dealer who he thought ripped him off.
Bix Beiderbecke: A celebrated cornetist whose playing foreshadowed cool jazz and bebop. He played with a number of groups, recorded prolifically and was said to be Louis Armstrong's only true equal as a horn player before dying at a young age.
Django Reinhardt: The first non-American jazz innovator, and one of the most influential guitar players of the 20th century. With the Quartet/Quintet of the Hot Club of France, he replicated swing with an all-string ensemble, inventing the sub-genre known as Gypsy Jazz.
Ella Fitzgerald: One of the most well-known jazz vocalists of all time, her range, accuracy, sense of swing, and the cheerful quality of her voice led many to consider her one of the greatest singers of the 20th century, period. Expect Vocal Dissonance (Sorry Ella). She was the singer in Chick Webb's orchestra and took over as leader after his death. After the swing era came to a close she remained popular and pioneered singing in a bop style.
Cab Calloway: One of the other Trope Codifiers of scat singing, like Louis Armstrong. He was one of the first African-American performers to make it big, performing alongside Al Jolson at one point. He was also known for his dance moves, and brought jazz to a wider audience by appearing in Betty Boop cartoons.
Glenn Miller: One of the most popular band leaders, he led his orchestra as one of the biggest record sellers from 1939 to his (literal) dissappearance in late 1944. His greatest hit was "In The Mood", not counting his work with the Andrews Sisters. Expect one of his pieces in any WWII setting.
Billie Holiday - Also known as "Lady Day", she is possibly one of the most famous jazz and blues vocalists of all time. Much emulated, her tragic life is as well known as her talent. She is often depicted in media, and even has a cult classic biopic starring Diana Ross. "Strange Fruit" by Abel Meeropol, her signature song, brought attention to the lynchings of blacks in the Deep South, and was voted by Time Magazine as the greatest song of the 20th century.
Bebop, Cool and Modal
Miles Davis: Jazz trumpet virtuoso started in bebop, went on to pioneer multiple styles of jazz (Modal Jazz, Cool Jazz, and Fusion, among others). His 1959 album Kind Of Blue is the best selling jazz album in history, with 1970's Bitches Brew not far behind. Many great jazz musicians, from the 50's to the 70's, and beyond went through his band for at least a short time.
Art Blakey: Brilliant drummer whose band, the Jazz Messengers, created almost as many big names as Coltrane's various lineups. His style of playing jazz is also probably the Trope Codifier for the hard bop that pretty much defines mainstream jazz.
Charlie Parker: Saxophonist whose virtuoso approaches to rhythm, harmony, and tempo laid the foundations of Bebop and revolutionized jazz (and music itself!) like few others.
Bud Powell: Pioneering bebop pianist and composer, regarded by those who know as one of the geniuses of jazz piano but a combination of drugs, alcohol and a police-inflictedhead injury caused him to have a Creator Breakdown, and he was seldom the same afterwards.
John Coltrane: Master saxophonist and spiritual thinker who covered nearly every jazz style of his time (even creating a few).
The Dave Brubeck Quartet: Redefined what could be done with bebop, bringing avant-garde polyrhythm and polyphone to the masses with such oddly-timed instant classics as "Take Five," "Blue Rondo a la Turk" and "Unsquare Dance"; pianist Brubeck was the second jazzman, after Louis Armstrong, to be featured on the cover of Time magazine (He would have preferred Duke Ellington got that honor instead and felt he himself was honored because he was white). They were also one of the first well-known integrated jazz bands — three white men and one black — and were known for refusing to play gigs in places where their bassist Eugene Wright would be discriminated against.
Bill Evans: Considered one of the most influential jazz pianists of all time. He eschewed virtuoso showmanship and fancy ornamentation, choosing languid, breezy sound colors and drawn out musical passages. The jazz ballade, "A Waltz for Debby", became an international hit, and a jazz standard. Lyrics have been added to the piece in many different languages.
Thelonious Monk: Best known not for his beard, his odd onstage antics, or his collection of unusual hats, but for his idiosyncratic style of playing — you have to be a really good musician to play that haphazardly and still make it come out exactly right. Also an inventive and persuasive composer; he only wrote about 70 tunes, but nearly all of them have become standards.
Charles Mingus: The angry man of jazz, absolutely brilliant and over-opinionated in every place that counted. Known for taking pot shots at other jazz musicians, being an outspoken social activist, inspiring The Who to trash their instruments on stage, and writing a guide for how to toilet-train cats. Also one of the great jazz composers after Duke Ellington (who he cited as a major influence), writing longer, more complex compositions that seamlessly brought together blues and more avant-garde influences (as a teenager growing up in Watts, Los Angeles, he studied Schoenberg and Stravinsky alongside Ellington) in addition to more conventional jazz "tunes" based on 16- or 32-bar progressions. He's the first- and only, so far - jazz musician to have his entire (gigantic) catalog acquired by the Library of Congress.
Dexter Gordon: A Tenor Sax phenom who helped spread bebop to other instruments.
Monica Zetterlund: A legendary Swedish jazz vocalist. She's most famous for singing jazz treatments of Swedish folk tunes and popular music. Her most famous recording internationally was the Swedish version of "A Waltz for Debby", "Monicas Vals", with the Bill Evans Trio.
Oscar Peterson: A Canadian jazz piano legend who was and still is often compared to Art Tatum in terms of virtuosity; indeed, Tatum was a major influence, but Oscar's style was more contemporary to the early bebop era of the mid 1940's (as opposed to the swing era of the 30's) while maintaining some of the more melodic idioms of swing as well as incredible ballad and blues playing.
Wayne Shorter: together with Sonny, one of Bebop's last living legends, a saxophonist that was and remains very influential as a member of Miles Davis' group, the seminal jazz-rock band Weather Report and as a solo performer.
Joe Pass: one of the most influential guitarists of bebop.
Vince Guaraldi: A famous jazz pianist who is most famous for his scores for the early Peanuts animated specials. For instance, his A Charlie Brown Christmas soundtrack has become a perennial holiday classic and many kids' first introduction to jazz. Despite his fame for the Peanuts score, his style was heavily influenced by Afro-Cuban Jazz and Brazilian music. Before he died, his later Peanuts scores experimented with harpsichord, Hammond organ, hard bop, fusion, and funk.
Chet Baker: as notorious and infamous, as brilliant as a trumpeter.
Ornette Coleman: Made the legendary Free Jazz which broke every single musical rule possible.
Weather Report: A jazz fusion band formed by keyboardist Joe Zawinul and the afformentioned Wayne Shorter, both members of Miles Davis' jazz fusion-era quartet. Among the band's best known recordings is the Grammy nominated 1977 album Heavy Weather, one of the best selling jazz fusion records of all time. During the late 70's and early 80's, the band's lineup famously included...
Jaco Pastorius: Widely considered to be the most innovative bass player ever. Pretty much every modern jazz bassist cites him as a major influence.
Herbie Hancock: Wrote three of modern jazz's standards — "Cantaloupe Island," "Dolphin Dance" and "Watermelon Man." His lineup on the Headhunters album more or less created jazz fusion by adding funk influences into the mix. The first artist to have a jazz-hiphop crossover hit with "Rockit", memorable now for its Mind Screw of a video.
Peter Brötzmann: German free jazz saxophonist best known for his blistering 1968 album Machine Gun, which remains one of the most formidable albums in jazz canon to this day.
Medeski Martin & Wood: Brought fusion into the 21st century with a mix of funk and hip-hop.
Wynton Marsalis: a controversial musician, but probably the most famous and popular living jazz musician (together with Sonny Rollins), who plays a more 'traditional' jazz, with heavy influences from anything up to the Bebop and Cool jazz era.
On the other hand, his similarly acclaimed brother Branford is much more open to new styles and experimentation - he played on a Public Enemy track, for starters.
The whole Marsalis family, really. Ellis, their father, is a pianist, and other brothers include a percussionist and a trombonist. They also play classical as well as jazz.
St Germain: a French musician, he's among the pioneers of Nu Jazz and the most famous exponent, combining eletronic music with jazz.
Gordon Goodwin's Big Phat Band: An American big band led by tenor saxophonist, pianist, songwriter and conductor Gordon Goodwin, the Big Phat Band has played just about every style of jazz and has included or collaborated with many of the big names in contemporary jazz music.
John Zorn: Eclectic and highly prolific saxophonist and composer best known as the bandleader for the avant-garde klezmer/jazz group Masada. Founded the experimental jazz and improv label Tzadik Records. The poster boy for the inverse form of Scary Musician, Harmless Music.
Kenny G: He has to be mentioned to some extent. An American saxophonist, Kenny G is probably the most successful jazz musician worldwide in terms of record sales, but he's probably the most controversial musician on this list. He's the best known exponent of "smooth jazz", a sub-genre which has been criticized by jazz critics and fansnote Virtually anyone who enjoys the music made by ANY of the musicians listed above would seriously dispute whether Kenny G can be called a jazz musician for being barely one step above Easy Listening lounge music. To his credit, though, he defines his own music as "instrumental pop" rather than jazz.
Brian Setzer: A bit of an oddball entry, he's done a lot to revive interest in big-band swing, including creating arrangements that add parts for lead electric guitar alongside the brass section, and making arrangements of classical compositions redone in a big-band swing style with electric guitar leading. The the resulting arrangement works and works well.
Jonah Dempcy (and his various pseudonyms): similar to the aforementioned St Germain, combines jazz with the various types of electronic music, creating an alternatingly darker and lighter style. A word of warning: hip-hop, dubstep, and house are in his musical vocabulary, and he will use them.
Sun Ra: His birth certificate states that he was born Herman Blount in the early 20th century Birmingham, Alabama, but Sun Ra would maintain throughout much of his later life that he was in fact a native of a far away planet. As such, his eccentric worldview and lifestyle would often overshadowed his extremely extensive body of music, which ranges from bop, to free jazz, to doo-wop. His worldview, a unique blend of black nationalism, science fiction, and magic realism, would prove to be extremely influential in both the musical and literary worlds, including George Clinton's Parliament-Funkadelic mythos.