I used to organize 'em by type, but I have too many pokemon in XY so it's too much of a hassle lol. My 3rd and 4th Gen boxes are still by type. I guess technically they aren't by "type" per say - more by area that the pokemon would live in. For example, I have two boxes labeled "Forest" in Sapphire, which includes things like beautifly, nidoran, rattata... and one named "Safari" which includes pokemon from the Safari Zone. I actually had separate "River" and "Ocean" boxes for water types that I thought looked like either fresh water or salt water critters. I had "Cave" for rock/ ground/ zubat etc., Volcano for fire-types, one box for cute pokemon that I thought would be more like housepets... etc. I mean, I was like ten when I played Gen 3.
Nowadays in XY, I have box 1 designated for any pokemon I'd typically need for battle - this includes my six level 80-100 pickup ambipom, my 5th and 6th gen IG teams, my HM slaves, my lvl 100 flame body talonflame (granted she's almost always in my party, but when she isn't...), my shiny false swipe sneasel, and my suction cups malamar for fish chaining, which fills that one box almost completely.
The battle box is whatever competitive team I'm using at the moment. The last box (immediately behind the battle box) is for competitive reserves. I don't have enough competitive pokemon to fill the box yet (especially with six in the battle box), so I can separate those that are "battle ready" and those that haven't been EV trained or leveled to 50 / whatever level they need to be for their particular moveset or evolution yet. Ideally I'll get a separate box for non-trained pokemon once it fills up.
I have one box for extra 5IV correctly natured pokemon for trading. It's always full, but I haven't gotten around to clearing another box yet so I try to keep it varied and send extras to my Wondertrade box.
My Wondertrade box right now is filled with 5IV pumpkaboo lol but usually it's just 4IV breeding leftovers. I'll fill the box and send them all at once, then pick through whatever I get in return.
Anything I get from Wondertrade with good IVs that I can breed and use the offspring competitively I send to one of my two breeding boxes for later use. They're also both full so sometimes they get mixed into other boxes. :/
I have two boxes reserved for MM egg hatching. I'll hatch two boxes at a time, then cull the resulting offspring for either future trades or Wondertrade. I'll keep trade of how many eggs I've hatched in the name of one of the boxes. Because I only hatch two boxes at a time, I just need to add 60 after I've filled them.
I also have two boxes for legends, one for shinies, one for vivillon (and a few flabebe) and one entirely filled with ditto.
I used to have a box for eggs that I'm too lazy to hatch, but I'm not allowed to do that anymore because I never hatch them LOL. I also used to have a box for pokemon that I need to evolve for dex entries, but I've completed the dex and therefore don't need it anymore.
Other than that, my boxes are sorted vaguely by "type" (see first paragraph lol), but as I completed the pokedex and lost room in my boxes, I have a few misc boxes and some pokemon that don't fit the type they're supposed to fit. I really need to organize 'em, but I'm too lazy.
And... yeah, that's that! It's a system that works for me, anyways! Wish I had more room, but Pokebank is too much room... so whatever. xD