I saw this thread when it popped up yesterday and was intrigued, but needed some time to think about it. 
Frame of reference: I was born in 1971.
1980: AC/DC - Back in Black (1980)
The first album I ever bought, it opened me up to rock music. I couldn’t get enough of it.
1982: Ozzy Osbourne - Diary of a Madman (1981)
I’d spent the next couple of years listening to some other rock, but a lot of top 40 stuff as well. Sometime around 6th or 7th grade I was gravitating more towards rock, and discovered Ozzy. I bought Blizzard of Ozz at the same time as this one, but Diary was the one that really spoke to me. I decided at this point to become a little metalhead.
1983: Rush - Signals (1982)
1983: Pink Floyd - Wish You Were Here (1975)
1983: Iron Maiden - Piece of Mind (1983)
As I got more into rock over the next couple of years, these three stand out as albums I really liked. I didn’t realize it at the time, but they are examples of my tastes gravitating more towards challenging, complex music, rather than plain rock like AC/DC, Ozzy, Led Zeppelin, Van Halen, etc. Don’t get me wrong, I loved those bands too!
1986: Marillion - Misplaced Childhood (1985)
This is the one that changed everything. If I was ranking these albums in order of importance, it would be #1. I’d heard “Kayleigh” on the radio, and thought it was cool, but it quickly faded from public consciousness. Sometime later, a friend played the album on the sound system at my school’s planetarium where we worked, and I was blown away. I immediately went out and bought it, and decided I needed more of this type of music. And thus my life-long love affair with progressive rock was born.
1986: Genesis - Nursery Crime (1971)
1986: Yes - The Yes Album (1970)
1986: ELP - Brain Salad Surgery (1973)
These were some of the first prog albums I bought. I was familiar with “I’ve Seen All Good People,” “Starship Trooper,” “Roundabout,” “Still… You Turn Me On,” and “Karn Evil 9” from the radio, so I bought TYA, Fragile , and BSS. I chose Nursery Crime as my first “real” Genesis album because I’d heard “The Musical Box” on Stonetrek, a weekly prog radio show in the Bay Area.
1992: Dream Theater - Images and Words (1992)
Most of the prog I’d been listening to over the years was from the '70s; at the time, there was little new prog that wasn’t “neo.” I heard “Pull Me Under” on the radio, and was intrigued, so I bought the album. Damn, mixing metal and prog, who’d a thunk it? I wouldn’t really call them “prog-metal,” more like “prog leaning towards metal,” but they opened the door to a sub-genre of prog that I love to this day.