To add a few specifics:

        Long Shot  De Bucket           Pioneers
        007                                               Desmond Dekker
        Funky Kingston                            Toots and the Maytals
        Liquidator                                     Harry J All Stars

Check these on You Tube, they will lead you to some great tunes

Some great suggestions: they take me back to my (misspent) youth. As a blanket suggestion: explore Trojan records, I remember that a lot of great reggae by less well-known artists was on this label.
They are still in business, celebrating 50 years.

these probably came out early in this millenium but have you heard the Easy Star Allstars covering popular concept albums in reggae style? They did Sgt Peppers Lonely Heards Dub Band and and Radiodread (a cover of Radioheads OK Computer) Both brilliant records.

Most of what I was going to recommend is already listed, but if you get stuck you can look out for the greensleeve albums.

The French love it! Look up French Reggae on YouTube it is really good stuff. It is often in English if you prefer.

Do you have a style preference? I think these are all between 1970 and 1990.

Albums:

May or may not be what you consider "pure reggae", but as I remember, there's not much dub, if any at all, in these:

The Wailers and I-Threes:

Bunny Wailer - Blackheart Man
Bob Marley and the Wailers - Exodus
Judy Mowatt - Working Wonders
Marcia Griffiths - Naturally
Peter Tosh - Legalize It
Rita Marley - Who Feels It Knows It
The Wailers - Catch A Fire

Uh... more than one genre:

Aswad - New Chapter
Black Uhuru - Anthem
Burning Spear - Marcus Garvey
Desmond Dekker and the Aces - Israelites.
Gregory Isaacs - Night Nurse
Max Romeo and the Upsetters - War Ina Babylon
The Mighty Diamonds - Right Time
Steel Pulse - Handsworth Revolution
Various - The Harder They Come (soundtrack from the film starring Jimmy Cliff

Toasting, which influenced Rap and Hip Hop. DJ Kool Herc, the Father of Hip Hop, was an immigrant with his family to the Bronx from Jamaica. His sister Cindy is credited as the First Lady of Hip Hop. Immigrants. They get the job done!

Dillinger - CB200
Eek-A-Mouse - Wa Do Dem
Yellowman - Mister Yellowman

Dub:

Augustus Pablo - East of the River Nile
Aswad - New Chapter of Dub
Big Youth - Screaming Target
Dr. Alimantado - Best Dressed Chicken in Town
Joe Gibbs - African Dub Almighty Chapter 3
Mikey Dread - World War Three
King Tubby and Augustus Pablo - King Tubbys Meet Rockers Uptown
Lee Scratch Perry - Roast Fish, Collie Weed and Cornbread
Lee Scratch Perry and the Upsetters - Super Ape
Upsetters - 14 Dub Blackboard Jungle
Upsetters - Return of Django
URoy - Version Galore

lmao

[muxicbeats.com]

Don't do it. Just say no!