I grew up with jazz, with my Dad being a huge jazzhead. In his student days in England he used to hitchhike all over Europe to listen to his heroes and imbued a huge love of the music in me. Artists I love include many that have already been mentioned.
Miles Davis - in addition to the albums mentioned, check out Sketches from Spain. Huge, huge musical sound, best listened to on a beach at sunset time.
John Coltrane - possibly the coolest jazzman of all time for me. Check out Soultrane, Lush Life, My Favourite Things and any number of live recordings. He played w lot with Miles Davis - notably on Kind of Blue and Milestones. Utterly mouthwatering.
Stan Getz - not necessarily always one of the top of the list for the purists but a great musician nonetheless. His "bossa nova years" gave rise to Latin Jazz and made the voice of Astrud Gilberto the most played, and abused, voice of the genre.
Herbie Mann - a sweeter flute you will not hear. His summertime was the first chune I learnt to play and for me, no one has come close.
Ike Quebec - Not very well known but the quintessential smokey jazz club sound with a gravelly melancholy that fucks you up - in a good way. One of my favourite albums of any kind of music is his Blue and Sentimental.
Other favourites include Monk, Charlie Mingus (another genius), The Dave Brubeck Quartet or Quintet, particularly Paul Desmond, Sonny Rollins, Dexter Gordon (oustanding) and the prolific and brilliant Bill Evans. Will try and post more later.