Depends on what sort of jazz you are into. Miles Davis played many different styles of jazz, some of which I love (his earlier stuff) and then he went off the deep end as far as I'm concerned and played very out there stuff. The 2 legendary jazz albums are Kind of Blue (with Miles and Coltrane) and Blue Train (with Coltrane, Lee Morgan, Curtis Fuller). You gotta get those, they are awesome. If you're like me and like the more straight ahead, bebop, blues type jazz check out these guys:
Trumpets:
Clifford Brown - greatest bebop trumpet player ever, don't even argue with me on this. Died tragically young.
Fats Navarro - He was playing bebop a decade before people knew it existed, he inspired Clifford Brown.
Lee Morgan - Early stuff is great bebop, esp his famous Sidewinder album. A Clifford Brown protegee.
Freddie Hubbard - Similar bebop style to Lee Morgan.
Dizzy - He's the Diz, nuff said.
Wynton Marsalis - young guy, albums worth checking out: Joe Cool's Blues, Standard Time Vol 1, any Lincoln Center Ellington Orchestra revival stuff he's doing
Roy Hargrove - Another young lion, he's young stuff is HOT. Check out: The Collected Roy Hargrove, Tenors of our Time, Parker's Mood <-- bass, trumpet, piano trio album playing all Charlie Parker tunes, its freakin good!
Nicholas Payton - another young lion similar to Hargrove and is amazing. Has New Orleans roots. Must have albums of his: Payton's Place, Gumbo Nouveux, Dear Louis.
Leroy Jones - very unknown, underrated. He is true to the New Orleans style of play. Very bluesy, very hip, very soulful. He's best known as the trumpet soloist for Harry Connick's Big Band.
A few others if you get bored with these: Thad Jones, Art Farmer, Clark Terry, Harry "Sweets" Edison, Roy Eldridge, Kenny Dorham, Snooky Young.
Sax:
Cannonball Adderly - One of the most inspiring alto bop players.
Coltrane - every loves him cept me. His later stuff is too out there for me, but his earlier stuff is on the spot (like Blue Train album)
Charlie Parker - set the standard of alto bebop playing.
Sonny Stitt - pretty underrated but totally amazing. Check out album Sonny Side Up with him, Sonny Rollins and a burning Dizzy on trumpet.
Eddie "Lockjaw" Davis - almost funny to hear play, real bluesy and cool.
Joshua Redman - Young lion. His early stuff is soooo good (he's gone pretty out there recently). Albums worth checking out: Live at the Vanguard, self titled one, Freedom in the Groove, Timeless Changes.
Antonio Hart - Phenomenal young lion alto player.
There a tons of other sax players who are great.
Trombone:
JJ Johnson: The absolute king of bebop trombone. In fact that's an understatement, he was the Emperor, the God of jazz trombone. He's the one that took a clumsy odd instrument that people couldn't play very fast or hip, and turned it into a bebop machine. Every trombone player to come after him was inspired in some way by JJ. Good Albums: The Eminent JJ Johnson (both volumes), JJ Inc. (my fav), Live at the Vanguard, any JJ and Kai album.
WYcliffe Gordon - very young, very aggressive player. He plays incredibly down and dirty, it's awesome. He was Wynton's sidekick bone player for a long time and you can check him out on alot of Wynton's Septet stuff, but Wycliffe's solo albums are ruthless as well! He has a duo cd with another bone player John Allred called Head to Head that is the best.
Steve Turre: Bone player on SNL band. Awesome player, also known for playing jazz on sea shells, and it's pretty hip.
Bass Players:
Ray Brown - the bass player legend.
Christian McBride - young guy, very agressive and awesome.
John Clayton - Big band leader, composer, good player.
Neils Orsted Pederson - One of THE most amazing bass players along with Ray Brown. White guy from Sweden, you'd be amazed at what he does. Long time sidekick to Oscar Peterson.
Piano:
Oscar Peterson - in my opinion the most amazing piano ever (and he's still alive and playing!). His technique is amazing, he bops like no other, utterly amazing, you can't overstate how good he is. Any album with him is freakin good, especially if it's live. All his live jam ablums from Montreux are nuts.
Gene Harris - this guy swings harder than any other mofo. He is the epitamy of blues piano jazz. He grooves on and on, check it out.
Benny Green - Oscar Peteron protegee, kind of a cross between Gene and Oscar, cant go wrong with him.
A list of some good big bands: Duke Ellington, Count Basie, Stan Kenton, Buddy Rich, Louie Bellson, Clayton/Hamilton, Harry Connick's, Airmen of Note, Army Blues Band, Thad Jones/Mel Lewis.
Hope this list is kind of helpful. I tried to put up a bunch of names of players you might not have otherwise heard of. I have alot of jazz, over 300 albums. Stuff I listed is a bunch of stuff that isn't weird, way out there, wtf are you playing? type of jazz. It's stuff that even if someone doesn't like jazz, they could handle and chill to it. The list's people put up are great places to start too, but Mingus and Monk and the like may be a bit weird at first. Wag's sax list is really good too.