I wouldn't say these albums "made me", but they all had impacts on a young me. Mostly in terms of expanding my horizons in one way or another from growing up in a small town in a dusty, prickly, out of the way corner of New Mexico (yes, even the Madonna and Beastie Boys).
Beastie Boys: "Licensed to Ill"
Madonna: "I'm Breathless"[1]
Enya: "Watermark"
Yello: "Stella" (Just wild creative stuff)
The Police: "Live!"
U2: "The Joshua Tree"
Indigo Girls: "1200 Curfews"
Peter Gabriel: "Secret World Live"
Dead Can Dance: "Within the Realm of a Dying Sun"
(I'm actually not sure which Dead Can Dance to pick. Once I discovered them, I picked up as much of their catalog as I could.)
[1] I probably wouldn't have bought this for myself, but my dad won it in a raffle during a showing of the Dick Tracy movie and promptly handed the cassette to me. At the end, they included "Vogue", but my favorite on it is the duet with Mandy Patinkin: "What Can You Lose":
https://www.youtube.com/watch?v=lAdzhgqNSdk&list=OLAK5uy%5FnpmZiX4TZ%5Fz2%5FugnQ%5FMvmtlgiKhat2JrA&index=9