The Cure
I discovered The Cure when I was a teenager, at the time still listening to Broadway musicals. I liked them right away but didn't want all my Mormon friends to know how dark I really was. As I got into college and away from all that I started to express myself. My biggest regret is not going to Denver to see the Disintegration show in 1989 (I had an LDS mission to prepare for, after all, and couldn't get distracted by worldly things).
In the 1990's I fully embraced my inner Robert Smith, just as he was going out of style. I have many other favorite bands and songs from that era, but The Cure is my only lasting obsession.
Oingo Boingo
Danny Elfman was a top 40 standard in the 80's (who can't love "Dead Man's Party"?), but when he did the Batman soundtrack I was hooked. I saw his last album tour in 1994 and used to just park my car late at night, in Provo, feeling opressed by Mormons, and crank up "Insanity."
Siouxsie & the Banshees
I fell for Siouxsie when she did the song for the second Batman. I knew and liked the band before that, but that song sealed the deal. I only regret not having discovered her 10 years sooner. Some of the best post-punk, pre-goth music ever made.
U2
Yeah, Bono's St. Rock Star. Yeah, much of their music is pop crap. But "Joshua Tree" was a profound album in 1987 and still moves me. Never could bring myself to go to a live show, but I'll always like their music.
Sinead O'Connor
"The Lion and the Cobra" changed my music universe in 1989. Such passion, such a voice! I got a radio DJ to dedicate "Jerusalem" to me 4 years later the day before I went to Israel for a study abroad. Damn ex-girlfriend stole the tape I recorded it on. "I do not want what I haven't got" came out when I was a Mormon missionary and I heard "Nothing Compares 2 U" at a mall and I made us stop so I could hear it all. I broke all the rules and bought the album while still a missionary.
Her later stuff just got weird, but "Universal Mother" was a nice bump till she just fell completely down.
Charlie Parker and Miles Davis
I decided I needed to understand Jazz. It was always this elite genre that intimidated me. So I got a book on the history of Jazz and another recommending recordings. I'm self-taught and know that I'm missing many good artists, but so far Charlie Parker and Miles Davis have just jumped out at me. Smooth sounds that transport you to another world.
NIN
"Pretty Hate Machine" came out while I was a Mormon missionary, so I missed some of the initial impact it made. When I got home and began rebuilding my personality it was the first album that touched that resentful, deep seated, angry part of me that I had so throughly buried for so many years. Later efforts have been hit or miss, but I can forgive him much because of PHM.
Suzanne Vega
"My Name is Luka" is trite these days, but its hardly her best work and did, in fact, have an impact back in the day. She's the best poet/story teller I've ever heard. Someone aptly described her voice as "fragile and minimalistic." I'll always wish I could command my language the way she does.
Counting Crows
A kind of crossover jazz/rock group, I didn't like them when "August and Everything After" came out. They seemed a bit whiney (I was into NIN and Nirvana at the time, too angry for a whiney band). Years later I got into them (after I calmed down a bit) and find them easy to listen to when I'm driving. They are great to sing along to.
Echo and the Bunnymen
Another 80's alt band I was peripherally aware of back then, but a few years ago I rediscovered some of their less-airplay'd gems and got hooked.
New Order
What can you say about one of the fathers of the club sound? "Substance" is still a very listen-able, dance-worthy, album.
Philip Glass
Was introduced to minimalism in the late 80's by my composer friend. Found it instantly appealing. I think it fits my obsessive nature. Koyaniskatsi and Powwaqqatsi were visionary. I fell off the couch a few years ago when songs from "Solo Piano" showed up on Battlestar Galactica.