I also like music that's complex and lyrics that have a lot of meaning, it gives me something to think about and makes me want to listen to it more than once. I used to be a big fan of classical (romantic) music, I liked Chopin and Beethoven the most. I also liked Irish folk music and classic rock & pop. But now as I've grown older, my music tastes have changed, now I like EDM, modern rock, indie pop/rock, some r&b, some old school stuff and country pop (not the cheesy stuff you hear all the time on the radio! None of that!).

I'm the same as @Meganemer4 , I find it difficult to like all/most the songs from an artist. That's why it's so difficult to answer which artist I'm a big fan of. The only singer I'd say I like all the songs from is Hunter Hayes and I like most of the songs from twenty-one pilots ('Semi-Automatic' describes INTPs perfectly!). Then there's particular songs I like from different artists - 'Thief' by Imagine Dragons, 'Stolen Dance' by Milky Chance, 'Yellow' by Coldplay, 'Lego House' and 'Photograph' by Ed Sheeran, 'The Locket' by Lauren Alaina, 'Satellites' and 'The List' by Reed Deming, 'I Need You Now' by Smokey Robinson, 'If You Don't Know Me By Now' - various artists, 'Perfect Storm' and 'Water' by Brad Paisley, 'Home' and 'Lost by Michael Buble, 'Live Like You Were Dying' by Tim McGraw, 'Do Something' by Michael West. Also a handful of movie soundtracks (Forrest Gump, The Boy in the Striped Pyjamas, Braveheart and Gladiator), Bruno Mars and Avicii songs.

So yep, my music taste is all over the place.

 

I grew up listening to classical, jazz, and sometimes rock and variety. I started liking music when I entered college, a friend introduced me to metal of all sorts. After that, I met two other friends who made me discover other genres. We discussed in lengths about what was likeable in each track. One of these friends is now an acquaintance, but has always been a highly logical mind, and the other got a degree in musicology, and turns out to be INTP (I can tell now that I'm used to MBTI, but he always has been =p). I don't see him that much anymore since he moved to Canada, but I still consider him a good friend.

What I realized, when talking with them, is that what I liked about music was not that the guitars were heavily saturated, or that it relied on lyrics. I liked the complexity of the music and how it lifts me and make me want to move. How expert the musicians were. How hard it was to systematize. I like to recognize complex patterns, and I like when it's so complex that I can't recognize them. I don't know. It just blows my mind sometimes.

Considering that, I gradually, and naturally started finding some metal genres to be tiring, or, sounding always the same. Similarly, I didn't like classical and jazz very much, since my parents only listened to that when I was growing up. I grew to appreciate a good part of them.
I also grew out of my complete hatred for hip-hop and derivatives, I can now appreciate some good hip-hop, some good rap. I appreciate the EDM part of electronic music, trap, dubstep (what people call "dark" dubstep nowadays, ugh), electroswing, hardteck.

I don't care for lyrics and vocals. As long as they don't change the nature of the music so much that they distract me from it, I don't usually mind them. I won't remember lyrics most of the time. It requires me to focus a great deal to even get what is talked about, and I'm not speaking of when I have to find hidden meanings in them. If I try to focus on lyrics I get distracted from the music itself and I don't appreciate it like that.
As a result, I dislike most variety. I dislike British pop-rock (Franz Ferdinand and alikes). I avoid radio stations. It's all the same, and doesn't promote the technical aspect of music enough for me.

 

I love twenty-one pilots and imagine dragons! *High fives*

 

I listen to classic rock, some indie rock, punk, some synthpop, some soul, funk and some opera. Mostly Led Zeppelin, Arctic Monkeys, Funkadelic, Bikini Kill, Black Sabbath, Fever Ray, and Bo Burnham. I think my type sorta affects what music I'm more inclined to like.

 

Mostly listen to sludgy, doomy, abrasive metal(ish) these days. Some of the bands I've seen over the last year or so are Godflesh (favourite) Neurosis, Black Cobra, Pallbearer, Torche, Conan, and Insomnium. Can find enjoyment in most music though, love any live concert.
The diversity in music listed here is interesting, doesn't seem to be any pattern to what INTP's like.