1. Sisters of Mercy - Floodland
In 1989, an online friend sent me a mix tape with "This Corrosion" on it, and I never looked back.
2. Peter Murphy - Deep (Cascade is a close second)
When I finally visited her a year later, she played this for me. It's probably a bit heretical, but I like him better solo than either Bauhaus or Love & Rockets.
3. Delerium - Karma
Semantic Spaces got me into them, and I later went back and learned to appreciate their earlier work, but this is the CD that I nearly wore out.
4. Peter Gabriel - Security
I still remember hearing "The Rhythm of the Heat" for the first time. Totally blew me away.
5. Enya - Watermark
As flemco mentions, she had a great sound and opened my ears to another whole category of music. Too bad she's basically done the same album about 6 times now. (Seriously: compare this album with her next two, and the styles line up pretty much track-for-track.)
6. This Mortal Coil - filigree & shadow
There are standout tracks on It'll End In Tears and Blood, but neither is the intense, epic journey of f&s.
7. Queensryche - Operation Mindcrime
8. Pink Floyd - The Wall
I spent a summer in college listening to these two albums pretty much every night. Good times.
9. A-Ha - Hunting High and Low
While "Take On Me" gets most of the mindshare, "The Sun Always Shines On TV" is the better track in my opinion.
10. Alphaville - Forever Young
Yes, the title track has gotten played to death, but the rest of the album is delightful 80s synth cheese. (Their next few albums are also good; Afternoons in Utopia is probably a better album, but I listened to FY first, and it has my heart.)
11. Ulcer - Crawl
A little band out of Las Cruces, NM, that never really went anywhere. But I roadie'd for them for a while, and this album is a great mix of their early favorites, some of their newer (at the time) material, and excellent production values.
12. Tori Amos - Little Earthquakes
I even saw her on this tour, but the music still stands on its own. I've liked bits and pieces of what she's done since -- and I'm incredibly happy that she continues evolving her music, instead of sticking with one style that happens to sell well -- but LE is still my favorite.
13. Depeche Mode - Black Celebration
While other of their albums are arguably superior (Music for the Masses, Violator), BC was the first one I listened to, so it's the one that I have the most attachment to. (Yes, I got into them relatively late.)
14. Garbage - Garbage
Between hearing "Vow" a year before the album came out, and then the number of people who asked me whether I'd heard of this neat song "I'm Only Happy When It Rains"...
15. Marillion - Misplaced Childhood
Their other stories in the "trilogy" (Fugazi, etc) are also good, but this one wins for the song arc and the first exposure advantage.
There are other albums that I'd take with me to the desert island, but I tried to pick out some that actually hit me. With most of these albums, I can still remember the first time I ever listened to them (20+ years ago, in some cases).