Oh so many, but I'll stick to stuff in genres I otherwise like - I could say "One Direction" but I'm not a raving fan of any other boybands so it's not really the point.
For me, the one that I find inexplicable is AC/DC. I like loud, guitar based rock. I don't mind it being simple and uncomplicated, I can cope with the dumb lyrics. Given other bands that I like, I should like AC/DC but I just don't. I've heard most of their stuff, certainly all the "classic" albums and a fair few of the, er, "less classic" albums. I've seen them live ferrchrisakes, and I can play a most of their riffs on the guitar (not hard..) but it just doesn't do anything for me. Even cranked up to 11 and after a few beers. No, nothing.
The Beatles, I also find it hard to get through a whole album of, but I'll give them a pass because, to an extent you probably "had to be there" for them, they moved the boundaries of what a pop band could aspire to create, then they went back into the studio and moved the boundaries again. I can't think of anyone (maybe, just maybe Bowie) since who have come from a pure "pop" position and been so innovative while still keeping their "pop" status. There's artists who've been "pop" and then "gone serious" but pretty much without exception them "going serious" has coincided with them "not selling many records anymore".
The Beatles were experimenting with unheard of studio trickery, their image, loads of drugs, exotic foreign instruments and tunings etc. and still shifting truckloads of records to the kids. So, in summary, I do 'get' the Beatles even though I may not particularly 'like' them.