Eric Clapton
Robert Cray
Los Lobos
David Byrne
Huey Lewis
Neville Brothers
Simon and Garfunkel
Tarika Sammy
Mahotella Queens
Brian Setzer Orchestra
Bonnie Raitt
Boz Scaggs
Leo Kottke
 
That's all I can think of right now. Plus, I used to see a lot of small-time local and regional bands when I lived in Minneapolis. Some of those guys were really good.

My list is a little Kooky 
There's more but once you see my list you will see I don't get out much these days .....
 
Free
Led Zeppelin 5 X
Gentle Giant
The Clash
Robert Plant w The Honey Drippers
Trini Lopez
Eric Clapton / various bands of his over the years
Les Paul
Don Ho
Dizzy G
Lou Donalson
Tito Puente
Stanley Jordan
Joe Pass
Herb Ellis
Edgar Winters w Johny W ..and Rick Derringer
Al De Meola
Mike Stern
The Allman Brothers ..w Dicky Betts
Herbie Man
Gino Vanallie
Chuck Wane Joe Puma
Savoy Brown w Kim Simmonds
Betty Carter
David Sanborn
Miles Davis
Bo Diddly
Larry Carlton
Grace Slick w Jefferson Airplane
Doctor Hook & the Medicine Show
Sid Jacobs
BB King
Sara Vaughn
Weather Report w Jaco
Steps Ahead
STUFF
Chicago
Mimi Fox
Jack Dejohnett Trio
Scandal w Patty Smyth
Bobby Blue Bland
Lucky Peterson
Roy Buchanan
Blood Sweat & Tears
Elvin Bishop
John Abercrombie
Ulf Wakenius
Oscar Peterson
Tony Bennet
Ella Fitzgerald
Kenny Burrell
George Benson w Earl Klugh
Dr Lonnie Smith w Jimmy Ponder
Dixey Dreggs
Herbie Hancock
Chet Atkins
Lee Ritenour
Three Dog Night
Chuck Berry
Nils Lofren
Diana Ross and The Supremes
Tod Rundgren
Taj Mahal
Wishbone Ash
Joe Walsh Band
Saturday Night Live Band w Elliot Randal & Paul Schafer...
Framton ..one on one time
Steve Miller ..one on one time...
Jorma K...
Larry Coryell w Eleventh House
Dave Liebman
Jack Sheldon
Buddy Rich
Count Bassie Band  
Every concert regardless of the genre that was done at Carnegie Hall...in 79 to 81..
The conductors I have seen during some of those concerts were Zubin Mehta , Sir George Solti, Seiji Ozawa ...


Other than that a few People I auditioned for in person that didn't give me the Gig ...
Chubby Checker , Meatloaf , Ritchie Havens and Michael Shreve ...
 
edit due to adding a few more
Kenny

Kenny,
 
I turned down offers to audition for Hall & Oats and Uriah Heap (both in ~1978). Hall & Oats were kind of rising up and I couldn't stand them and Uriah Heap was trying to make a comeback of sorts.
 

I've updated my post (#10) as the old bean has remembered more.

Kenny's list reminded me of one I saw when I was very young: Herb Alpert and the Tijuana Brass.  I saw a lot of Classical stuff when I was young, but don't remember much of it now.

Bold = numerous times
 
REM
The Smiths
The Cure
New Order
Echo & The Bunnymen
Pavement
Pixies
Radiohead
Cathernine Wheel
Sisters of Mercy
The Mission UK
Wilco
Siouxsie & the Banshees
Tool
Clan of Xymox
Pink Floyd
Fang
Dead Kennedy's
Psychedelic Furs
Sugar
Bob Mould
Chili Peppers
Soundgarden
Live
Camper Van Beethoven
Cracker
 
 
 
 
 
 

Waaaay back machine!
Boston
Nils Lofren
Kiss
Peter Frampton
J Geils Bank
Foghat
Rick Derringer
Lynrd Skynrd
Alice Cooper
Ted Nugent
Rolling Stones
John Cougar
Joe Ely
George Thorogood
The Who
Loverboy
Journey
Fleetwood Mac
Jefferson Starship
The Ramones
The Kinks
Foreigner
Doobie Bros.
ACDC
Sammy Hagar
Montrose
Blackfoot
REO Speedwagon
Nightranger
Styx
The Babys
John Waite (opened)
Dokken
Judas Priest
Scorpions
Van Halen
Motley Crue
David Lee Roth
Iron Maiden
Rainbow
Ozzy
Heart (opened)
Black Oak Arkansas (opened)
Cheap Trick (opened)
Blue Oyster Cult
Black Sabbath
ELO
Aerosmith
Neil Diamond
Diana Ross
Dire Straits
Prince
Bryan Adams
John Hiatt
Vince Gill
Collective Soul
Keith Urban
Glen Campbell
Hall and Oates
Pink Floyd (orig. Wall Tour)
The Police
The Eagles
Jackson Browne
Elton John
ZZ Top
Cyndi Lauper (opened in Tokyo)
Guns & Roses
 
 
I'm sure there are more.

These are the best:
 
Paul MCartney
James Gang
Cat Stevens (yes, he was actually quite good)
Yes
Ringo Starr (a really fun show)

Those I have a conscious memory of, there are some I also choose to forget.

Pink Floyd several times
Hawkwind with different line ups
Rick Wakeman
Phil Collins
Deep Purple
John Dankworth (Saw him for free as his drummer borrowed my drum kit)
Courtney Pine
Jean Michael Jarre (Docklands)
Thin Lizzy (Another free one as the band turned up without road crew myself and few others help lug the gear in)

A shameful second addendum to my list.
 
The Bay City Rollers, several times - I kid you not, before they hit the big time they were on the club circuit and used to play occasionally at a night club I used to frequent. (We went to this club mainly because they were not too fussy about age restrictions on admission and buying drink). They were a run of the mill band playing mostly covers, then suddenly they appeared on Top of the Pops with a new tartan boy band image and became an "overnight teenybob sensation".