Groundbreaking albums. Any genre.

Not necessarily the very best but those that opened up a new direction and influenced many.
Miles Davis - Bitches Brew
John McLaughlin with Mahavishnu Orchestra - Inner Mounting Flame
Pink Floyd - Dark Side Of The Moon
Dead Can Dance - Spleen and Ideal
John McLaughlin/Paco de Lucia/Al di Meola - Friday Night in San Francisco 
Deep Purple - Machine Head
John Coltrane - Giant Steps
Black Sabbath - Self Titled First LP
King Crimson - In The Court Of The Crimson King
Sex Pistols - Never Mind The Bollocks
Joy Division - Unknown Pleasures
Stravinsky - The Rite Of Spring
Ornette Coleman - The Shape Of Jazz To Come
Fripp & Eno - No Pussyfooting

Beatles: Sgt Peppers, Rubber Soul
Mother's of Invention
Velvet Underground
Pink Floyd
King Crimson
Peter Gabriel - Security and So
Paul Simon - Graceland
Radiohead - Kid A
Jefferson Airplane - Surrealistic Pillow
Cream - Disraeli Gears
Jimi Hendrix - Are You Experienced?
 Glenn Gould, 1955 Goldberg Variations
- Elvis Presley: s/t debut. He and his band mixed black R & B with white Hillbilly, creating Rockabilly and all the Rock ’n’ Roll that followed. Buddy Holly, Carl Perkins, Jerry Lee Lewis, and others followed Presley’s lead.

- Bob Dylan: Blonde On Blonde, in which he infused Rock ’n’ Roll music with abstract surreal poetry, turning a teenage music into an adult one. IMO the most influential Pop music artist of the 20th century in the long term, more so than Elvis or The Beatles. You may disagree. ;-)

- The Byrds: Sweetheart Of The Rodeo. Chris Hillman and Gram Parsons turned the McGuinn-led Folkie group into a Country one, introducing the modern Rock audience to Hillbilly music. Hugely influential album to Rock musicians, though those of us paying attention had already began to discover Hank Williams, Lefty Frizzell, The Louvin Brothers, The Carter Family, Bill Monroe, and all the other Hillbillies Elvis and the other Southern white boys were hearing on the regional radio stations in the late-40’s and early-50’s.

- Cream: Fresh Cream. Basically a Blues band (though Jack Bruce and Ginger Baker were more Jazz influenced) who introduced long Jazz-type improvisation to the Rock audience. Whether or not that’s a good thing is a matter of opinion. After hearing The Band’s debut album Music From Big Pink, Eric Clapton himself decided it wasn’t.

- And of course The Band: Music From Big Pink. Amongst a "certain" group of young Rock-based musicians, the biggest game-changer of them all. For those who "got it", the rules of the game had been suddenly changed, the rug pulled out from underneath them. Everyone I knew had to start over, learning to approach music and it’s making in an entirely new way: Playing from the "outside" towards the center, rather than the opposite, if you know what I mean.

There are plenty more albums that can be cited, none more so than Are You Experienced by The Jimi Hendrix Experience. That band and album created a music template still imitated today, but for me the it was short-lived (I loved them the first time I saw and heard them live in ’67, but was bored the second time in ’68). It and they now sound dated to me. You may disagree. ;-)
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I’ll go with Ogden’s Nut Gone Flake.   
Mahavishnu Orchestra wasn’t a groundbreaking LP. They toured that before and after. Saw them do play it twice. Saw John again at The Cubby Bear with his guitar synth. Holy Moly.
McLauphlin’s Electric Dreams gets my nod.
Or Adventures In Radioland.
Floyd toured the Dark Side... over a year before they cut it with Alan Parsons. The ground was quite disturbed by then.

Rush Moving Pictures
Pink Floyd The Wall
Tool Undertow (changed prog metal forever)
Yes Fragile
Led Zeppelin 1,2,4, Physical Graffiti 
King Crimson (Agree with above)
Jefferson Airplane Surrealistic Pillow
Jimi Hendrix Are You Experienced...

The list could be somewhat endless as we go through genres.
Elvis Presley-Elvis PresleyVelvet Underground & Nico-The Beatles-Sgt Pepper'sThe Who-My GenerationThe Ramones-The RamonesThe Smiths-The SmithsBlack Sabbath-Black SabbathThe Beach Boys-Pet SoundsMarvin Gaye-What's going onDavid Bowie-The rise and fall if Ziggy StardustMiles Davis-Kind if blueHerbie Hancok-Head hunters.....and many oters

.....King Crimson-In the court,
Stevie Wonder-Songs in the key if life,
The Byrds-Fifth Dimension, 
Michael Jackson-Thriller,
Pink Floyd-DSOTM,.......


Terry Riley’s A Rainbow in Curved Air. 
Talk Talk’s Spirit of Eden. 
Both of those changed expectations of what recorded sound should sound like. 
The Melvins
mekong delta
sex pistols