My list would not be a list of who is the best, as O-10 has said that's a silly and impossible question to answer. My list, is a list of the difference makers. The seminal figures in Jazz. Just for fun, so put those daggers away!
1. The Creators - the people in and around New Orleans that created this music. I don't have a clue as to who they were, Jelly Roll Morton's protests notwithstanding. Without them, there is no Jazz.
2. Louis Armstrong - Took the music out of New Orleans and gave it to the world thru his talent and personality. A true ambassador. He may have been the only person that could do that.
3. Duke Ellington - elevated the music to a very sophisticated level. Showed it was more than just music for dance and speak-easy joints. Also a great Ambassador. Went on a world tour sponsered by the US State Dept. Played in the Soviet Union. One of the great composers of the 20th century. Period!
4. The be-bopers - Parker, Dizzy et al. Infused jazz with a new direction and engery at just the right time. Kept the music modern. Also expanded the audience.
5. Miles Davis - Took the music several new directions. Was involved in all the post bop movements. Brought in the young crowd as part of the audience. Fusion, cool etc..
6. The Players - these are all the people that give such enjoyment just by their high standard of play. here you will find players like, Sonny Rollins, Julian Adderly, Lee Morgan, Horace Silver and all the thousands more that have sustained the music thru the years.
7. Girl Singers - Gave Jazz a 'voice'! And what voices! Can't have any list about Jazz without Ella and Billie. They also opened the door for women in Jazz. As performers and as part of the audience. And like Brazilian sports super stars, they are recognized by their first names. Ella, Billie, Nina, Abbey, Sarah, Carmen, Dee Dee, They are, and that is, soooooooooooooo cool..
8. John Coltrane - Instrumental in taking Jazz a new direction that led to the Free and Advant-Garde movement. Wrong turn in my opinion. But great does not mean good. He was an important figure. Gotta give him his due.
9. Thelonious Monk - Unique. In a class by himself. Others wanted to follow, but COULD NOT. One of the great talents with a one of a kind musical instinct and personality. Made the cover of TIME, no small feat for a Jazz player. Once chewed Coleman Hawkins out. He makes the list for that alone. :)
10. The Germans - This refers to the immigrants from Europe, mostly German, mostly Jewish, who had the foresight and appreciation to record this great music. To encourage the players, to see things in the players that they didn't see in themselves. If not for them, we would have nothing to play on our gear. Because the powers that were at that time, had no interest in, or respect for, black music, and the players didn't have the wherewithall to do it. Jazz lovers owe them a debt that cannot be repaid.
For those that demand this - IMHO! :)
Cheers