Having completely undercut myself by highlighting the meaningless nature of my list, let's take a look. As I said, I'm not claiming these are the best albums ever, just the ones most influential on me. We're talking albums, not songs or musicians. Many jazz and soul artists whom I revere are not on this list; while I may love certain songs, there is not one entire album that I love.
I have listed these in chronological order, which is roughly how I encountered them. Since I was born in 1963, the early ones belonged to my Dad or my older siblings. I didn't encounter the Beatles until high school, but I was instantly hooked (That's also where I found Stanley Clarke, The Gap Band, Cameo and the Brothers Johnson). It looks like 1979 was a huge year, but some of those albums I picked up a few years later.
[Editorial note from 2006: This list was first posted in September of 2000, when the last entry was DJ Shadow's Endtroducing.... I've added a couple albums that clearly belong. You will note that I have nothing from the past four years. That's not to say that there aren't worthy contenders that could be added, but it's hard for me know what those ones are until a little time has passed. Plus, as the last few years have shown the growth of the digital music age, I just listen to fewer albums. But I may add some eventually.]
Feel free to submit your own lists to thepopview (at) gmail.com. Please remember: you're not submitting your favorite artists, but favorite albums. There is a difference.
After my list, I have included some links to other lists, for comparison's sake.
Jonah Jones Quartet - Swingin' on Broadway (1957)
Erroll Garner - A Night at the Movies (1964)
The Monkees - Headquarters (1967)
The Beatles - The Beatles a.k.a. The White Album (1968)
Blood, Sweat & Tears - Blood, Sweat & Tears (1969)
Stevie Wonder - Where I'm Coming From (1971)
Supertramp - Crime of the Century (1974)
Kraftwerk - Trans-Europe Express (1977)
Talking Heads - Talking Heads '77 (1977)
B-52's - The B-52's (1979)
Boomtown Rats - The Fine Art of Surfacing (1979)
The Clash - London Calling (1979)
Elvis Costello - Armed Forces (1979)
Joe Jackson - Look Sharp! (1979)
Madness - One Step Beyond... (1979)
Pink Floyd - The Wall (1979)
Joan Armatrading - Me Myself and I (1980)
Robert Palmer - Clues (1980)
Pretenders - Pretenders (1980)
Prince - 1999 (1982)
Split Enz - Time and Tide (1982)
Minutemen - Double Nickels on the Dime (1984)
The Pixies - Surfer Rosa (1988)
De La Soul - Three Feet High and Rising (1989)
Jules Holland - World of His Own (1990)
Nirvana - Nevermind (1991)
Urban Dance Squad - Life 'n Perspective of a Genuine
Crossover (1991)
Hole - Live Through This (1994)
Portishead - Dummy (1994)
Soul Coughing - Ruby Vroom (1994)
Ben Folds Five - Ben Folds Five (1995)
DJ Shadow - Endtroducing... (1996)
Stereolab - Emperor Tomato Ketchup (1996)
Tipsy - Trip Tease (1997)
Blinker the Star - August Everywhere (1999)
Soulwax - Much Against Everyone's Advice (1999)
Ben Kweller - Sha Sha (2002)
N.E.R.D. - In Search Of... (2002)
Regina Spektor - Soviet Kitsch (2004)
Alice Smith - For Lovers, Dreamers and Me (2006)
Amy Winehouse - Back to Black (2007)
Vampire Weekend - Contra (2010)