Jazz as an entire genre could be classed as music I don't 'get' - apart from Monk and latin stuff like Tom Jobim, nothing has really reached out & grabbed me. Someone upthread said something to the effect of 'if music is worth spending time with, it won't be immediate' - I disagree, good music should have an effect on the first listen: that doesnt preclude new interpretations on repeated listens over time, but the initial spark should always be there.
The 60s canon - Dylan, Beatles & Beach Boys go over my head, esp. Dylan. The Byrds are class, and Love are good in places - but I 'get' them, I can hear how the forces around them are pulling the music into strange shapes, even if they don't always deploy that effectively. The Doors I'm seriously getting into recently, and developing a parallel theory that they are the unacknowledged godfathers of Krautrock which you can read more about
here (scroll down).
Bowie is an interesting one to bring up - because there's so many different sides of him to 'get'. For years I loved the Berlin stuff but the Hunky Dory era material left me cold - not helped by being raked over by Blur so cack-handedly in the 90s. But I got Ziggy Stardust recently and that absolutely blew me away, so much better than Hunky Dory.
Stuff I used to get but now don't - Nirvana. Lyrically, Cobain's navel-gazing is just the flipside of 80s selfishness. I also find now that musically, it doesn't work as rock music - the guitar is too weedy to get that monolithic stoner rock immensity, and the rhythm section doesn't flex enough to get that 60s power trio suppleness that Hendrix and the Stooges had. I'd way rather listen to Pearl Jam than Nirvana now.