I've often thought that if you were to judge my identity solely based on my shelf of comics, you'd think I was a teenage boy. It's full of One Piece, Eyeshield 21, Hellboy, Blade of the Immortal, etc.
I confess, when it comes to the fighting-type shounen - all the big three you mentioned, for example - I'm more likely to watch the anime. Fighting really comes off well in animated form, what with there being a lot of motion going on all the time. So while I haven't read a whole lot of the big three, I've watched a lot of them. I watched Naruto up through the first 20 episodes of post-timeskip - and then quit, because I lost interest. Likewise with Bleach - I like to pretend the story ended after the first Soul Society-arc. After that, it just kind of goes bland for me.
One Piece, though... I may be some 20-odd episodes behind, but I love One Piece with a passion too fiery for words. <3 I've not only watched nearly 700 episodes of it, I've rewatched the first 300 of those episodes multiple times. It is dorky and weird and ridiculous and awesome and oh my gosh does Eichiiro Oda ever know how to suckerpunch me in the heart when I least expect it. One Piece proves, again and again, that you can have a main character who likes to stick chopsticks up his nose and pretend he's a walrus, and still deal with themes like slavery, oppressive governments and the right to live our lives how we choose.
I think One Piece holds the record for cartoon that has made me cry the most. I'm all feels and nowhere to put them when I watch One Piece.
As for more recent stuff... The internet's all fired up about One Punch Man lately, but I haven't had the time to try it out yet. I hear good things, though.