I'm going to break the rules!
1960s
Winner: The Beatles - Sgt. Pepper's Lonely Hearts Club Band
A Day in the Life is still one of my favourite Beatles songs, though I break the rules and consider it a collective tour de force rather than a simple Lennon or McCartney song (to be honest, I can't make up my mind on which song of theirs is my favourite). My father used to listen to this song constantly when I was younger before my parents divorced and it always gives me warm fuzzy feelings even after he has already passed on. She's Leaving Home is also another favourite to play on the ukulele and sing with my family.
Runner Up: Miles Davis - Kind of Blue
Realistically released in 1959 but fuck it. I can not for the life of me ignore the tracks Freddie Freeloader and Blue in Green. All Blues makes me want to dive in to a bathtub filled with dopamine and pass out in bliss. People say it is Miles' best album for a good reason. I'm sorry Beach Boys.
1970s
Winner: Pink Floyd - Wish You Were Here
Too many people will nominate Dark Side of the Moon but screw it. Shine On You Crazy Diamond is beyond epic in nature, and Welcome to the Machine is always played no matter how many times I put this album on. My brother does an awesome rendition of Wish You Were Here so I get all karaoke on that without hesitation.
Runner Up: Electric Light Orchestra - A New World Record
A surprise entry! Oh my! I would have nominated any Led Zeppelin or Elton John album throughout this era, but Jeff Lynne did my Welsh paternal->maternal surname proud by pumping out an incredible pop album of its time. Telephone Line is an emotional classic, Rockaria is beyond measure, and Livin' Thing is the poster child of 70s pop music. My favourite track is easily Shangri-La though, as was my father's. Uncanny!
1980s
Winner: Talk Talk - Spirit of Eden
Another controversial choice! Most people assume The Colour of Spring to be Talk Talk's biggest album in the critical circles but Spirit of Eden does it for me. The Rainbow makes me want to fly up in to the clouds and puff on them, while Wealth makes me want to adopt the fetal position until I die.
Runner Up: U2 - The Joshua Tree
Where the Streets Have No Name will, forever and always, be my favourite U2 song both in studio and live format. There is something electrifying about it no matter how many repeated chords The Edge plays -
the live at Slane Castle version (after a supremely magical "All I Want is You" might I add!) is easy to testify to this and if it doesn't raise the goosebumps then you are no human. The track With or Without You is also an immediate classic and an easy reason to understand why U2 play it all the time at concerts.
1990s (i.e. SO FUCKING HARD)
Winner: Radiohead - OK Computer
An easy suggestion some might add. I had been listening to Radiohead prior to its release, The Bends essentially forced me in to what I was during my adolescence years (was born in 1983) and it was no fault of my own that I became immediately attracted to Paranoid Android after the brilliance and subjective whispers of Fake Plastic Trees and Street Spirit. That should not deny the fact that I have loved Radiohead since 1995 and have continually loved every single song of theirs throughout. Exit Music makes me cry during a drunken tirade, I sing Karma Police with my brother without any qualm when he shows me his new guitars, No Surprises always needs to be played, and I have a special kindred bond with my older sister due to our shared love of The Tourist.
Runner Up: Jeff Buckley - Grace
Beyond measure. Simply beyond. The album and the artist changed me during a time when I felt so hopeless and alone. Easily the keystone when I stopped caring about what people thought of me and my choices in music (I was surrounded by friends who only listened to punk) and helped me get through the peer pressure bullshit. Last Goodbye will forever remain a classic, Lilac Wine is always sung whenever I take a drop of plonk, and Lover, You Should've Come Over is one of the greatest love songs ever played.
[honourable mentions because 1990s was too hard: Boards of Canada - Music Has the Right to Children, DJ Shadow - Entroducing..., X Japan - Dahlia, Ben Folds Five - Whatever and Ever Amen, Sigur Rós - Ágætis Byrjun.]
2000s
Not possible.
Instead here are the albums over the last 10 years which have impressed me to the point of quivering shakes.
Radiohead - Kid A (2000)
The Avalanches - Since I Left You (2000)
Coldplay - Parachutes (2000)
Quantic - The 5th Exotic (2001)
Elbow - Asleep in the Back (2002)
Explosions in the Sky - The Earth is not a Cold Dead Place (2003)
Express Rising - Express Rising (2003)
Mono - Walking Cloud and Deep Red Sky, Flag Fluttered and the Sun Shined (2004)
Boards of Canada - The Campfire Headphase (2005)
The Evpatoria Report - Golevka (2005)
Mono & World's End Girlfriend - Palmless Prayer / Mass Murder Refrain (2005)
Sigur Rós - Takk... (2005)
Grizzly Bear - Yellow House (2006)
Guillemots - Through the Windowpane (2006)
Mono - You Are There (2006)
The Cinematic Orchestra - Ma Fleur (2007)
Radiohead - In Rainbows (2007)
The Evpatoria Report - Maar (2008)
Grizzly Bear - Veckatimest (2009)
Karnivool - Sound Awake (2009)
Grey Reverend - Of The Days (2011)
Radiohead - The King of Limbs (2011)