The way you get started with Dub reggae is by looking at rhythm sections.
Sly n Robbie (Abyssinians, many titles by Sly n Robbie)
Lincoln "Style" Scott and Errol "Flabba" Holt (Roots Radics, Gregory Isaacs, Eek A Mouse, Israel Vibrations)
start with those guys.
Traditional dub started out as instrumental tracks put out by bands for singers to audition or practice too. The dub tracks became popular with Reggae DJ's who used the dub tracks to lock beats and create these perpetual grooves in the sixties. This sound was made popular by guys like Prince Fari, and I-Roy. Also check out King Tubby and Lee Scratch Perry.
The these cats started toasting (that really fast precussive rap style of singing) over the top of the dub tracks
Yellowman (the king in my opinion)
Eek A Mouse
Capleton
Yami Bolo
Chaka Demus
Musical Youth
Sizzla
Beanie Man
Shaggy
Soon producers (like King Tubby) started putting together these tracks that were meant to be spacy and hypnotic and this eventually grew into what it is today where the reggae is played with a live mixer. Lee Scratch Perry is considered the godfather of this format. He has inspired people like Mad Professor.
Here's a list of dub stuff to check out.
Abyssinians
Aggrovators (w Bunny Lee)
Al Campbell
Alpha and Omega
Aston "Family Man" Barrett (this is the Wailers bassplayer - Cobra Style- holy crap this is a good album).
Aswad
Augustus Pablo
Baaba Maal
Barrington Levy
Big Joe
Big Youth
Bill Laswell (Dreams of Freedom - Ambient Translations of Bob Marley, Meets the Roots Tonic - this is Matisyahu's band)
Bim Sherman
Black Uhuru
Bleechers
Bobby Ellis and Deadly Headly
Bobby Kalphat
Bruce Ruffin w DJ Spooky
Buju Banton (more of a dancehall guy but most dancehall is toasted over heavy dub tracks)
Bunny Wailer
Burning Spear
Capleton (especially with Yami Bolo)
Carl Moore
Carlton Livingston
Chicken Chest (ripping toaster)
The Clash (Radio Brixton, Sandinista (produced by Lee Scrach Perry), Super Black Market Clash)
The Congos
Cornel Campbell
Culture
Dave Ruffy
Delroy Williams
Dennis Alcapone
Dennis Brown
Derrick Morgan
Dicky Burton
Digital Mystikz (Good modern dub stuff)
Dillinger
Dirty Harry
Disciples
DJ Scruff
Dobby Dobson
Augustus Pablo
Don Carlos
Dr. Alimantado
Dry and Heavy (a rhythm section of Osaka, Japan. Dry=drums, Heavy=bass * this is not to be taken lightly- very very good stuff)
Dub Is A Weapon (more of a live act - check out there shows on Archives.org)
Dub Pistols (nice blend of dub reggae and hip hop)
Dub Syndicate (Style Scott/Flabba Holt - huge in the dub world)
Dub Trio (pushing the envelope of Dub. This is a mash of speed metal, punk, thrash and dub reggae. Very good stuff)
Sly Dunbar (the Sly of Sly/Robbie)
Easy Star All Stars (remake of albums - Dub Side of the Moon, Radiodread (Ok Computer - very good stuff)
Eek A Mouse
Earnest Ranglin (get some live stuff - borders on jazz)
Errol Alphonso
Errol Dunkley
Errol Holt (This is Flabba)
Errol Walker (big influence on Bradley of Sublime)
The Ethiopians
Fabulous Five (Ooh! Ahh!)
Fat Freddy's Drop (sick stuff out of New Zealand)
Fela Kuti (not really dub reggae but important heavy groove music from Africa)
Freddie Mc Gregor
Freddy McKay
Fredrick Galliano and the African Divas
Frisco Kid (dancehall but good stuff)
Garnett Silk
General Echo (Sly and Robbie)
George Boswell
George Faith
Gladiators
Gladstone Anderson
Glen Brown (King Tubby)
Glen DaCosta
GREGORY ISAACS (HIS NAME IS IN CAPS FOR A REASON!!!!!!!)
The Heptones
The Hippy Boys
Hopeton Lewis
Harace Andy (In The Light/In The Light Dub = A+ dub)
Hot Steppers (check these guys out - it's our very own TB playa Burning Skies on bass)
Hugh Mundell
I Roy
Ijahman
The Immortals
Impact All Stars
Ini Kamoze
Iration Steppas
Israel Vibrations
The Israelites
The Itals (Herbs Pirate is a great great song)
Jackie Mittoo
Jacob Miller
The Jah Boys
Jah Lion
Jah Lloyd
Jah Shaka
Jah Stitch
The Jahlights
The Jamaicans
Jimmy Riley
John Holt
Johnny Clarke
Johnny Osbourne
Johnny Nash (Not dub but an unsung hero of reggae in my opinion)
Junior Byles
Junior Delgado
Junior Dread
Junior Murvin (huge influence on The Clash)
Keith Hudson
Keith Rowe
Ken Boothe
King Jammy (Did a great album with Dry and Heavy)
King Midas Sound
King Tubby (essential in the world of dub)
Kingstonians
Kode 9
Lacksley Castell
Larry Marshall
Lee Scratch Perry (check out Experryments at the Grass Roots of Dub)
Linton Kwesi Johnson
Linivil Thompson
Little Joe
Little Roy
Lloyd Chambers
Lloyds Allstars
LLoyd Parks
Lone Ranger
Long Beach Dub All Stars (They've got some ok dubs)
Lucky Dube
Mad Professor (understudy of Lee Scratch Perry - amazing to hear live)
Martin Campbell
Matisyahu (not to be taken lightly. The can definitely dub out)
Max Romeo
The Meditations
The Melodians
Michael Prophet
The Mighty Diamonds
Mighty Revelations
More Relations
Morewell
Morgan Heritage (Electioneering track on Radiodread is great)
Neville Tate
Nick Holder
Niney The Observer
Noiseshaper
The Observer All Stars
The Orb (not straight dub but heavily influenced by it)
The Overnight Players
Pablo Moses
The Paragons
Pato Banton
Paul Blackman
Peter Broggs
Peter Tosh (Legalize it is not a dub album but essential reggae)
Pratt All Stars
Prince Far I
Prince Jammy
Prince Jazzbo
Ranking Dread
Ras Michaels
The Revolutionaries
Rico Rodriguez (Roots to the Bone - this guy was the horn player for The Specials)
Rockers All Stars (compilation of various players)
Roots Radics (AKA Dub Syndicate - this is their band when singer fronts them - like Gregory Isaacs, Eek A Mouse, Israel Vibrations)
Rootsman
Rupert Reid
Ruts DC
Sanchez
Scientist (In the vain of Mad Professor)
Senya
The Silvertones
Skream
Sly and Robbie
Sly and the Revolutionaries
Soul Syndicate
Soundclash
Steel Pulse (only because if you see these guys live you'll understand. The just endlessly jam)
Sub Version ft. Paul St. Hiliare
Submission
Sugar Minott
The Tamlins
Tappa Zukie
Taxi Connection
Taxi Gang
Tayo Meets Acid Rockers Uptown
Thievery Corporation
Thomson All Stars
Tommy McCook
The Twinkle Brothers
U Brown
U Roy
The Upsetters
Val Bennett
The Viceroys
The Wailing Souls
Wayne Smith
Winston Williams
Yabby You
Yellowman
That should do ya to start.
EDIT: I owe a lot of this music to Burning Skies. This guy is one of the kindest guys on TB.