In primary school and Key Stage 3 I mainly listened to chart pop and rock music. I listened to the Now! That's What I Call Music albums a lot.
But eventually I grew bored of pop as it seemed to be getting blander and blander. Then, one day my brother played his FIFA game downstairs for some reason, and you know how the FIFA games always have a soundtrack consisting of indie pop and rock music? Well, I listened to some of the songs and discovered some more songs from the bands. I was still listening to the aforementioned alt rock bands, but a lot of 'indie-like' bands like Fitz and the Tantrums, Passion Pit, Mew and Animal Collective joined my collection.
Then in 2014 I joined another forum and had a little peak at the music discussions to see what kind of music the other users liked, being curious. A lot of these bands I never heard of, but I took a little listen to them. When I stumbled across the Irish shoegazing band My Bloody Valentine, I immediately fell in love with them and decided to explore shoegaze and dream pop, and discovered more great bands like Slowdive, Asobi Seksu, Ride, Lush and Cocteau Twins.
I also found some post-rock bands: Mogwai and Godspeed You! Black Emperor. I did remember listening to Sigur Ros before and enjoyed them, and since they were considered post-rock, I expected these other bands to be sound them. I was very wrong, but they very quickly grew on me (especially GY!BE. They're definitely one of my favourite bands)
And then I discovered Swans, an American experimental/noise rock band. When I first heard the album To Be Kind, I must admit, I didn't know what to think of it. Parts of it had me questioning whether or not it was music. But then something inside me told me to listen to it all again, and then more Swans songs from other albums. And now I love them.
TL;DR: My music taste went from pop and alt rock to indie. But nowadays I like post-rock, shoegaze, dream pop, and a bit of noise rock. And I don't think I can ever go back.