Great Saxophone Artists and Albums

I'm looking for well recorded masterpiece of saxophone albums. Can you recommend a few artists and their albums. I was familiar with Kenny G's - that was over 10 years ago. Any other different styles and genre of saxophone performers?

Kenny G? Hopefully you were only joking.
Anyway, if you want to hear virtuoso saxophone beautifully recorded, I recommend Stan Getz "The Lost Sessions".
Cannonball Adderley - Something Else, Autumn Leaves, Cannonball Takes Charge

Sonny Rollins - Tenor Madness, Saxophone Colossus, Way Out West, Rollins Plays for Bird

Charlie Parker - The Immortal Charlie Parker, Charlie Parker Live at Birdland, Bird at St. Nick's

John Coltrane - Blue Train, Coltrane, Soultrane, Lush Life
Wow, there's so much available, here's a few.
Dexter Gordon, "Doin Allright" "Dexter Gordon Ballads" "Tower Of Power"
Sonny Stitt, " Constellation" "Sonny Stitt With The Oscar Peterson Trio"
Cannonball Adderley, "Things Are Getting Better"
Lucky Thompson, "Tricotism" "Lucky Srrikes"
Pepper Adams, "10 to 4 At The 5 Spot" " Motor City Scene"
Gerry Mulligan, "Night Lights"
Charlie Rouse, "Unsung Hero"
Frank Morgan, "Mood Indigo" " Listen To The Dawn"
John Coltrane, "Bags and Trane" "Giant Steps"
Harold Land, "West Coast Blues" "Harold Land in Ney York"
There's much more.
Assuming you're asking for Jazz, here are a few living artists—

Branford Marsalis - any album. Perhaps more talented than his more famous brother. Contemporary, yet well grounded in tradition.

Joshua Redman - any album. Creative, fresh, distinctive, expressive, inspired. . .

James Carter - any album. Best recording quality of the three, yet all are excellent. Carter is edgier, crosses stylistic boundaries and blends in contemporary pop influences.
Any album by Ben Webster
You can always check out these more recent names:
Chris Potter
Gerald Albright
True as others saying once you dig on Sony Stitt, Canobal Auderley, Lee Konitz, Yan Garbarek, Michael Brecker, you'll understand that Kenny G deserves no attention as musician. The saxofone alphabet is HUGE and full of great legends! Hopefully you'll slowly understand jazz.
For ligher sax music perhaps Boots YaketiSax Randolph would make much more sense vs. Kenny...
other coltrane releases- black pearls, coltrane
hank mobley- soul station, turnaround, dippiin'
dexter gordon - go and whatever album has tanya on it
stanley turrentine- jubilee shout
cannonball- live in sanfran, why am i treated so bad(first side rocks just as hard as any rock show
I gotta say ditto for Branford. He is a giant in terms of tone and control. He has ULTIMATE control, especially in very soft passages. I don't like all of his stuff, but damn, he is good and can play any and everything.
Gerald Albright (live at Birdland West) and Kirk Whalum (For You) Saw them play together, what a great show. Top notch players for many years.
Johnny Hodges is hands down one of the finest Sax players. He played a lot with Duke Ellington. Johnny Hodges has many albums on the Verve label. Also, Grover Wahington Jr. "Mr Magic".Julian Cannonball Adderley played with Miles Davis a lot. Gerry Mulligan, Ben Webster , Coleman Hawkins anything by these guys.Also,David Sanborn "Voyage". Paul Desmond played with Dave Brubeck. Gene Ammons is also high on my list of favs. And last but not least for now is Stanley Turrentine...Awesome SAX!
O and PLEASE don't mention Kenny G's name when talking about great Sax players....ROFL
Thanks for the recommendations. I had limited experience in saxophone musicians and Kenny G happens to be the one I know of. His performance is ok. Good to know there many other great saxophone players and albums.

I'll definitely explore and get a few albums to start with. What are the different types/ genre of saxophone music besides Jazz? Thanks.
My personal favorite among active musicians is Branford Marsalis - as other have suggested. He has a huge range of musical interests and can play anything. His concerts and recordings are a delight and never fail to satisfy.
If you want to listen to something trippy and different,
Try John Klemmer
What are the different types/ genre of saxophone music besides Jazz?

Saxophone is most closely associated with the Jazz and Rock genres. There are plenty of sub-genres that fall within the umbrella of Jazz but that is another discussion. A better way to look at the saxophone is to get to know the different types of saxophones and who plays which. Generally the types are: soprano, alto, tenor and baritone. Get to know how these look, sound and who plays each. You are doing pretty good if you can tell an alto from a tenor by ear. Might be hard for a novice but not for an experienced listener. You will really be doing good when you can tell the difference between two alto players by ear (for example Paul Desmond vs Art Pepper). Yes, they both played alto, but each had his own "sound." Ditto for any other tenor players, soprano players, etc. Approach it this way and you will never get bored.

Two guys worth checking out but not previously mentioned in this thread: Dave Liebman and Mark Turner.
The saxophone has been incorporated into 20th century classical music. However, if you want to hear something different and gorgeous, try Bach's Art of the Fugue by the New Century Saxophone Quartet
Excellent recommendation by Gsm18439. The sound of a schooled saxophone quartet bears an uncanny similarity to that of a pipe organ, and while Bach sounds good on just about any instrument, it can sound particularly beautiful played by saxophones (and organ, of course). For more recorded classical genre saxophone listen to:

Ravel- Bolero
Mussorgsky/Ravel- Pictures At An Exibition
Milhaud- Creation Of The World
Glazunov- Concerto
Prokofiev- Romeo And Juliet
Prokofiev- Lt. Kije
Gershwin- An American In Paris
Rachmaninov- Symphonic Dances

Brandford Marsalis also recorded an album of classical works for saxophone "Creation" which includes the Milhaud and is highly recommended.
I'll try to add some lesser known ones to the list here.

A stunning recording with terrific baritone sax (along with flute and cowbell, lol) playing by Sahib Shihab (formerly know as Eddie Gregory): Sahib Shihab & The Danish Radio Jazz Orchestra by Danish Radio Jazz Orchestra
Warne Marsh, "Ne Plus Ultra", also terrific recording and playing.
David Murray - "Ming"
World Saxophone Quartet - "WSQ Plays Duke Ellington"
Bobby Watson - "Love Remains"
Lou Donaldson - "Blues Walk"
Stan Getz - "Bossas and Ballads"
James Carter - "Chasin' the Gypsy"
Joe Henderson - "Mode for Joe"
Bill Barron - "Hot Line"
Pharoah Sanders - "Thembi"
Yusef Lateef - "Eastern Sounds"
While most of the recommendations here are great , they mostly pertain to "jazz".Something a bit different is the work that Jan Garbarek has done with the Hilliard Ensemble.Really different and really quite cool- a glacial sax tone interweaving over choral music from the 16th century.2 albums , both on ECM. Just somethng else to consider.YMMV as alwyas.
I'm a big fan of the record Duke Ellington Meets Coleman Hawkins. Hawk's almost full-track solo on Mood Indigo is one of the greatest four minutes of tenor playing ever recorded (in my totally biased opinion), and his horn is prominent throughout the session. Plus you get the DE orchestra still playing about as well as it ever did. It's a Rudy Van Gelder recording, so the piano sounds a little truncated, but on the whole the recording quality is excellent.
Houston Person - Art & Soul, To Etta, etc.
Well recorded:
Joshua Redman, Spirit of the Moment - Great live album, really cooks
Jeff "Tain" Watts, Detained at the Blue Note - Phenomenal with Marcus Strickland and Kenny Garrett

Masterpiece saxophone albums:
John Coltrane, A Love Supreme - One of the greatest in the history of jazz
Sonny Rollins, The Complete Prestige Recordings - A master musician

Honorable mention:
Hank Mobeley, At the Cafe Bohemia, with Art Blakey, Horace Silver, Kenny Dorham
Phil Woods, More Live - A great sax player, a little more laid back, great recording
Houston Person "Soft Lights" and Scott Hamilton "Nocturnes and Serenades". Some of the best tone quality for digital sax that I have ever heard as well as great music.
Here are a few more to consider; Art Pepper, Wayne Shorter, Stanley Turrentine, Hank Mobley.
One problem with the question you (OP) have posed here is that the sax can go so many ways that it's safe to say that there are great sax recording that you'll love and great sax recordings that you'll hate.

Given the Kenny G reference, I'll stick with mainstream melodic playing (tho more widely admired songwriting) and suggest Coleman Hawkins "Body and Soul". You can leave some of the more adventurous material for later.
"Play the Right Thing" by Lou Donaldson.

I saw him live a few years back at the Village Vanguard in NYC and became a fan.
Some additional suggestions:

Branford Marsalis-Eternal
Stan Getz- Bossas and Ballads; Getz/Gilberto; Anniversary; People Time
Charles Lloyd- The Water is Wide
Eric Alexander-Gentle Ballads I-V
Paul Desmond-Antigua
John Coltrane-Blue Train; Coltrane Plays the Blues
Ben Webster - "At the Renaissance" - fabulous music and hard to accept it was recorded in 1960. Only problem is finding a copy.