Really good topic. And difficult to answer - it requires quite a bit of introspection and synthetic thinking.
In my early childhood, I didn't really listen to music and wasn't exposed to much music because my parents didn't really have big passion for music. My dad loves and loved back than Dire Straits and Rolling Stones, mom listened to some mexican mariachi stuff, but they very rarely played music in house, don't really know why. So, when I was a kid I used to hear that stuff, but very rarely and I wouldn't say it influenced me much. I did find some "best of " Shadows LP and I used to play that constantly when I was about 11. Not much else - but this I liked, especially the guitar tone. My journey really started in about 1994 when I was 14 years old when I heard Guns'n'roses on MTV. I was fascinated by both music and image and I taped all their videos on VHS and watched that constantly. Similar soon happened with Metallica. But shortly after that I started high school and discovered Nirvana. I soon collected their albums on tapes (taped from friends) and together with Nirvana started listening to Soundgarden, Sonic youth, a bit of metal such as Sepultura (but really on the side - I wasn't that much into metal). At the end of high school I got really sick of the electric guitar sound and didn't know what to listen to. Then purely by accident, I was in a used CD shop and saw an album whose artwork struck me. I didn't know anything about this band, but I bought the CD solely because of artwork and packaging. It was The Downward Spiral by Nine Inch Nails. This was another big moment in my development. Upon first listen, I didn't know what to make of it. I didn't like it nor dislike it, it felt difficult but also fascinating. I put it aside for a couple of months and didn't listen to it. Didn't listen to anything during this time, I was a bit sick of music. Then one evening I got the urge to listen to music, and something was very strongly telling me to reach for the NIN CD. Put it on, listened through the whole thing carefully and that was it. It struck me as a most brilliant piece of music I've ever heard. I realized that music doesn't need to have choruses, doesn't need to rely on instruments, can be highly conceptual etc. From there I sought after all the other similar bands, which led me also to "industrial music" - first more popular stuff like Skinny puppy, Front 242, Frontline assembly, but later also more avantgarde stuff like Throbbing gristle. Since Trent Reznor always talked about Aphex twin and Coil - I got into them, which led me to Current 93 and all that esoteric english music. Fell deeply in love with that stuff any this broadened my view of music immensely.
Now from that point I got into all kinds of avantgarde music (Stockhausen, Xenakis, Riley, Reich), electronic music (Autechre, Pan Sonic, Oval), minimalism, I started listening to more adventurous modern guitar music again (Keiji Haino, Sunn 0))), Earth, Melvins, Swans...), discovered classic late 60s early 70s band like Pink Floyd, King crimson, Jethro tull, Frank Zappa etc, discovered all the wonderful krautrock stuff, primarily Faust, Guru Guru, Cluster, Popol vuh, Tangerine dream, Klaus Schulze. Also discovered there's nothing to be ashamed about in liking good pop - I discovered Kate Bush, Bjork, much later Joanna Newsom, Bonnie Prince Billy... My taste is now very wide, but I also tend to stick with a fairly low number of bands I love most of all...that's how I function, I can't love many things intensely and simultaneously.
Jazz I really don't get and don't like. I really like freeform rock so it's weird I couldn't get into stuff like Albert Ayler, Cecil Taylor and such....mainly because of the very sound pallette, I believe. I like dirty, grungy, distorted, broken sounds. More classic jazz I really don't like...I'd like to get into it, but can't. I feel much more affinity to classical music than to jazz, but wasn't able to get properly into it either by now. I really like Penderecki and Arvo Part but that's all very modern as well...it's not "classical classical". I really like Shostakovich. But most of classical seems hopelessly romantic, culturally distant and irrelevant and unrelatable to me...even emotionally. Emotionally, I often find it as something very unstable...one moment it's delightfully happy and then it gets down and soppy, and then it's all in love and playful and I find that unbearable and neurotic. I like composers who maintain emotion. I like more gloomy atmospheres and darker moods. But classical remains my fascination and I really feel I'll get to understand it one day.