Coltrane's A Love Supreme and Davis's Kind of Blue

I love these two classic "albums". I was hoping someone could give me five or six other, well recorded, must have classic jazz albums (musicians) that I should have in my collection. I am spoiled and would want them to be relatively well recorded.
you could list many here....5 that would be no-brainers might be;

Billie Holliday, Songs for Distingue Lovers.

Ben Webster, Live at the Renniasance

Ellington, Jazz Party in Stereo

Ellington-Armstrong, Together for the First Time

Johnney Hodges, Blues-a-Plenty

all classics and all wonderfully recorded with inspired performances.

if you can get the Classic Records 45rpm versions (Analog Productions for the Webster) that would be the best way to hear these....but in any format they are excellent.
Cannonball Adderly "Somethin Else"

Sonny Rollins "Way Out West" "Saxaphone Colosus"

Lee Morgan "The Sidewinder"

Herbie Hancock "Maiden Voyage"

John Coltrane "Ballads" "Blue Train"

Miles Davis "Sketches of Spain"

Eric Dolphy "Out to Lunch"

So many more.....have fun!
miles' - relaxin', blue moods, bags' groove

dolphy - iron man

coltrane - crescent, giant steps, alternate takes

thelonius monk - straight, no chaser; criss-cross; brilliant corners

when you want to get more adventurous:

art ensemble of chicago - 'les stances a sophie', people in sorrow (+ lots more, esp. the late 60's early 70's stuff)

evan parker - toward the margins, breaths and heartbeats (+ lots more... but this stuff is way out there...)

sun ra - too much to list...

and, if you can tolerate lo-fi:

billie holiday - the golden years (vols. 1 + 2)
Coltrane - Giant Steps
Coltrane - Blue Train
Davis - Sketches of Spain
Davis - Milestones
Coltrane - Village Vanguard Sessions
Hancock - Maiden Voyage
The suggestions already given are great, but I would also recommend from Horace Silver-Song For My Father, the Stylings of..., and The Cape Verdean Blues.

I also like Stan Getz /Charlie Byrd-Jazz Samba.

In reality the list is endless. :-)

The Coltrane album called "Coltrane" on Impulse is often overlooked, but has some of the best really intense blowing you'll hear from him. Then his Ballads album, and his album with Johnny Hartman, show you what he can do in a completely different direction. I've listened to all 3 of those records some many times I've lost count, and still love them.

Also sometimes overlooked is the last Miles Davis quintet (with Wayne Shorter, Herbie Hancock, etc.). Two of my favorites of that period are "ESP" and "Nefertiti". Great, great tunes, and incredible interplay.

I love Thelonius Monk and have for 40 years, but finding the right album to start somebody with is not so easy. His albums can be a little inconsistent, and his approach puts off some people, for a variety of reasons. If it's still around, a compilation called Ballads, which consists of Riverside material, is the best intro I've ever found, and even as someone who likes the individual records, I have really, really enjoyed that compilation--very well chosen. That having been said, I bought the whole Riverside box, and listening to large parts of that over and over as well. I would say his live albums generally are safe bets.

Finally, Bill Evans' live material from the Village Vanguard in the early 60's is as classic as jazz ever gets, although it's quite a bit "straighter" then the other stuff we're talking about.

There is tons of fabulous stuff out there...what a great chance to discover good things!
All of the above postings were great and no one has mentioned Charles Mingus... It sounds like you like "cool" or "smooth" jazz. Can you elaborate about what you like to listen to...
To end I'll mention Oliver Nelson's Blues in the Abstract Truth... A must..
Coltrane - Blue Train
Miles Davis - Birth of the Cool
Bill Evans - Waltz for Debby
Ella Fitzgerald and Count Basie - On the Sunny Side of the Street
Ella Fitzgerald - The 40th Birthday Concert
Wynton Marsalis - Standard Time
Oscar Peterson Trio - We Take Requests
"It sounds like you like "cool" or "smooth" jazz"

I very much dislike anything that begins to sound like phoned in "elevator" jazz. If Kind of Blue by Davis is cool than that is what I like. But I also listen to everything from Anthony Braxton to Roscoe Mitchell To Masubumi Kikuchi, so it doesn't have to be simple or smooth. I want to thank everyone for their suggestions. I have most of the Coltrane stuff...and about 30 Miles Davis cd's. I guess another way to ask what I am looking for is: If you had to pick one or two masterpiece, must have albums by a jazz icon, which would it be? In other words, which Adderly album, which Hancock, which Monk, Silver, Mingus, Rollins, ad infinitum. Mostly from the 60's and 70's as that is an era that I don't know much about with jazz (Too busy listening to Steppenwolf and Jefferson Airplane!). I want to thank everyone for their suggestions so far...I am making a list! Thanks, Jim
Miles Davis- Sketches of Spain
John Coltrane- Blue Trane
Duke Ellington/ Loius Armstrong- Together for the First Time
Sonny Rollins- Way Out West
Art Pepper- Meets The Rythm Section
Sonny Rollins- Tenor Madness
John Coltrane- Lush Life
I second Bill Evans "Waltz for Debby" and would add "Live at the Village Vanguard," part of the same series of concerts.
Johny Hartman and John coltrane is one of the greatest jazz albums IMO and it's also well recorded....these two were at the top of their game when they recorded this....would be on my Desert Island list.
"Somthing Else" Cannonball Adderly, "Go" Dexter Gordon", "Sidewinder" Lee Morgan, Saxaphone Colossus" Sonny Rollins, "Moanin" Art Blakey, "Soul Station" Hank Mobley.
John Coltrane--Crescent; Dexter Gordon--Our Man in Paris; and from the guy who in my opinion is the most underrated jazz player of the last 60 years, James Moody--Last Train From Overbrook
"Masada" by John Zorn. Awesome all around, with sonics to "die for". Soaring, lyrical, and heartfelt. It will blow you away!
Given what you already like, I'd recommend:

Ornette Coleman - The Shape of Jazz to Come
Charles Mingus - Three or Four Shades of Blue
Michel LeGrand - LeGrand Jazz
Check out stuff that falls under the category "Hard Bop". I think that will get you where you want to go. (lots of good suggestions in the above, however).
You asked which Mingus,

Well Mingus Mingus Mingus
the Black Saint & Lady Killer are my 2 favorites. Love them above & beyond & sound quality is amazing. I rate all my LPs and few get the Amazing and these did.