Lets not debate who is Rockabilly and who isn't either. I will start with the Stray Cats who are one of my favorites. Anyone who has seen them live will sure agree with that.

Stray Cats
Reverend Horton Heat
Some Misfits sound a lot like rockabilly (listen to Angelf*#k)

I'm not very knowledgeable about the genre, but from what I do know Reverend Horton Heat's gotta be my fave. I really like their song "Liquor, Beer and Wine."

Rev. Horton Heat
Gene Vincent
Carl Perkins
Elvis Presley (The Sun Records Years)
The Flametrick Subs
Hillbilly Hellcats
Bill Haley & The Comets

Forgot to add The Cramps. I love Bikini Girls with Machine Guns.

Some considered the Stray Cats to be gimmicky, but I have always been blown away by Brian Setzer's guitar playing. "18 Miles to Memphis" is awesome stuff. And you are right, the two times I saw them live I had a blast. I usually like my rockabilly with a touch of twang.

The originals:
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Johnny Burnette Trio
Gene Vincent
Eddie Cochran
Billy Lee Riley
Bobby Fuller Four
Collins Kids
Ronnie Self
The Phantom
Dwight Pullen
Johnny Powers
Bill Haley & His Comets
Jack Scott
Joe Bennett & The Sparkletones
Buddy Holly & The Crickets
Bill Allen
Bracey Everett
Bob Luman
Ric Cartey
Johnny Carroll
Mickey Hawks
Benny Joy
Ersel Hickey
Art Adams
Warren Smith
Tyrone Schmidling
Johnny Kidd & The Pirates
Gene Summers
Wayne Walker

Neo-Rockabilly:
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Stray Cats
Polecats/Tim Polecat
13 Cats
Restless
The Pharoahs
The Rapids
Francine
Roughnecks
Darrel Higham
Levi Dexter

Psychobilly:
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The Meteors/P. Paul Fenech
The Quakes/Paul Roman
Milwaukee Wildmen
Tranquillizers
Nekromantix
Mad Sin
Brigitte Handley
Batmobile
Guana Batz
Dead Kings
Hellmaniacs
Krewmen
Long Tall Texans
Skitzo
Torment
Astro Zombies
Godless Wicked Creeps
Chibuku
Gorilla
Spellbound
Hangmen
Go Katz
Radiacs
Radium Cats
Bea Pickles
Coffin Draggers

Other/Punkabilly:
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The Amazing Crowns
Reverend Horton Heat
Atomics
Mike Ness (the solo albums)