I am going to keep mine to music from my childhood to early teenage years. I had to think about this one for a couple days. (also I might want to edit this later so feel free to not copy and paste this)
Neil Diamond - My mother loved his music and it was often the soundtrack of my 80s childhood (along with some of the stuff my dad really liked, like America and CCR, but I will have to go with Neil if I had to pick one). I will forever be a huge fan of his music and I feel like he instilled in me a bit of a love for a good melody.
Nirvana - They were the first "cool" band that I ever liked. I actually got Nevermind because of the Weird Al parody. When I heard that riff... I was sold. One of my best friends and I would play the crap out of their discography (among way too much other stuff to list here and only pick five of) and I still have my cassette copy of In Utero sitting on my shelf in my home office with my other tapes, new and old.
the Beastie Boys - I did not get into the Beastie Boys until a bit after Check Your Head was released. I had two uncles who are only like 6 and 7 years older than me, and they both had good sized CD collections - full of so much good stuff and a variety of it (especially Sam's collection). They would let my cousin and I listen to their stuff and look through it, and found out about a lot of shit from doing that and reading their old Spin and Rolling Stones from over the years. I grew up in the country - but not like it is where they are from. They are from a place with like zero red lights. 300 people. Anyway, I was able to check out stuff like Guns N Roses, Faith No More, NWA, Sonic Youth, Pearl Jam, Nirvana, RHCP, Dr Dre, Alice in Chains... Basically their house was a candy store for me when I became interested in music in 1992. I always thought the Beastie Boys were the coolest. I tried to dress a bit like them in junior high and would rap the lyrics with my friends. Thankfully I was able to see them live at Virgin Fest 2007 and then again at their Bonnaroo set in 2009. I wish I was old enough to go to shows during their Ill Communication or Check your Head days...
NoFX - I would have to say this was the first punk band that I heard and really enjoyed. Young teen me dug the hell of Punk in Drublic... it was rebellious, it didn't give a fuck, and most importantly to shape my punk taste for at least the next decade, it sounded pretty good in the production department. I had heard some 80s punk that sounded like crap and was not sold on them... But when my slightly older neighbor brought over Punk in Drublic - I was hooked. After that I loved bands like Lagwagon, Swinging Utters, Down By Law, Bad Religion, Wizo, Frenzel Rhomb...
nine inch nails - The final band was hard to choose, but i guess I will go with nin. In seventh grade I was hanging out a lot with Tammy, who was in my grade and a childhood friend of my best friend/neighbor. Tammy's house was cool. Her mom would let us drink Schnapps and once took me to another town to go to a mall without my parents permission (I told her it would be fine, I got in trouble). Tammy gave me my first CDs, before I had a CD player (Smashing Pumpkins - Today single with Hello Kitty Kat and Obscured on the B-side and the La Sexoristo album by White Zombie). She was also into crazy (to me as a junior high student) music that I started to get into. Her favorite band was nine inch nails. She had the shirts. All the releases. I believe Broken was the first one I listened to and fell in love with, but also Pretty Hate Machine and the Downward Spiral. She also was down with a lot of the alternative stuff from the time, like Afghan Whigs and Matthew Sweet, and I became a fan as well. Post script: when we got to high school she became a Christian and gave all of her CDs to myself and the mutual friend I mentioned, and gave us all of her nine inch nails band t shirts and videos and posters and basically all the devil shit... I think this phase lasted for a while. We quit being friends, she moved off, but now I am friends with her on Facebook and she seems normal. Back to nin, this was the first really dark music that I got into, and I think this colored my tastes to the present. I have seen nine inch nails three times so far and plan to keep going.
runner up: Pantera
Pantera was the first heavy band that I heard and liked. I ordered the Crow soundtrack off of BMG or Columbia House, and the first time I listened to it, with one of my friends, we immediately went to the music catalog to find more of their music with one of us saying "Can you imagine a whole album like this???" Before that Metallica, Guns N Roses, and MAYBE when our older neighbor played Iron Maiden, which I personally thought was lame till recently, was the heaviest stuff. Far Beyond Driven was out (I guess this was 1994 or 95) and it was ordered and devoured. I started playing music with my friends around 1996 and Pantera was definitely a big influence in the heaviness and style of the music we were doing. The mail order method ending up being how I was able to get music, in my tiny town with a bs music shop across the river charging 18 bucks for a damn CD.
But this is still leaving off bands like Prodigy, that made me start listening to electronic music - or Aphex Twin a man who's music was played at crucial points, or Modest Mouse helping me get through depression post tragedy or Cloud Cult helping me through my first breakup with someone I dated for more than a couple of years, or the joy I get from the Polyphonic Spree... Or the Strokes, when I heard their debut I started migrating from listening to mostly dance music to mostly rock music... Or Radiohead... When I saw them at MPP in 2003 I started going to rock shows instead of raves/electronic music events...