My (very intricate) system will probably come off as incredibly odd, but I find that it works very well for me.
In X and Y, I have four different unofficial categories for Pokémon; Team/Competitive, Pokédex fodder, Legendary Pokémon, and breeding reserves. My first box is reserved solely for the Pokémon that I used to play through the story (and yes, I used so many different species that they all do take up an entire box to themselves) This box is simply called 'Team'.
Next come my five boxes of competitive-level Pokémon, with beneficial natures, perfect IV's, special egg moves, EV training, etc. The first two boxes are filled with ones that are done, good to go, I could equip them with items and then drop them in the battle box at any time and be a-ok. The third has Pokémon that have the natures/IV's I want, but haven't been EV trained yet or aren't fully evolved or at level 50, and the last two competitive boxes have Pokémon that I want on my competitive teams, but haven't been bred yet. All of these boxes carry the tag 'Warrior'. Following this is a single box devoted to storing any Shiny Pokémon I've found during my gameplay. However, this box is only for Shiny Pokémon without competitive natures/IV's/Abilities/moves. I have three shiny competitive Pokémon; Gardevoir, Vaporeon, and Butterfree, and these three live in the Warrior boxes with their fellows. And if anyone wants to ask: no. These three are not available for trade under any circumstances.
The next boxes, which take up the bulk of my space, are all Pokédex fodder. They contain the final evolved forms of every single Pokémon in the 'dex, and are kept around in case I need to breed anything special that isn't on my competitive list, or I need a specific nature and there's a chance a Pokémon from their egg group has that nature and is lurking in these boxes. Pokémon in these boxes aren't arranged by number, but rather their habitat. It's a habit I picked up when Ruby and Sapphire came out, and it just kinda stuck. I feel that if most of these Pokémon are going to be stuck in a box for most of their lives, then they should be comfortable at the very least. Thus the boxes are categorized by biome, starting with Forest and Field Pokémon (which takes up three boxes on it's own), then City, then Savannah, then Desert, etc. Within each box Pokémon are organized according to level, with the strongest at the top and the weakest at the bottom.
After all the Biome boxes, there's a separate box devoted simply to all 18 Vivillon Forms, labeled 'Vivillon', which really isn't important. Following these are boxes that hold all of my Legendary Pokémon from previous generations. There isn't any order to them at the moment, they're just all tossed together in a huge hodge-podge.
After that comes the breeding resource boxes. The first one is kind of a holding pattern, where I can move Pokémon around and plan out how to specially design a Pokémon by breeding natures and IV's onto it. For example, currently I'm working on a Sassy Poliwag with Swift Swim and 4 Perfect IV's in HP, Def, Sp. Atk, and Sp. Def and a Speed IV of 0 for 117jokes. To do so, I found my non-competitive Vaporeon, which has a Sassy Nature, my female Dewgong, my Eevee with a 0 IV in his Speed stat, my HA Poliwhirl, and my 6 IV Ditto and placed them all in the box in the order that I'd need to breed them with one another to get the desired result. This box allows me to keep track of each stage of planning a Pokemon's breeding, and keep everything nice and tidy.
The next (and second-to-last) box is marked as 'Airlock' and it's where I do all of my transfers to and from Pokémon Bank. I just like being able to put everything in one spot to make transferring Pokémon easier. And finally, there is my trade box, directly before the Battle Box. Whenever I finish a custom order for my thread, I move the result here, to avoid any possibility of it getting mixed up and accidentally released or Wonder Traded. It's also strategically located so that when I begin a trade, I just have to click over once from where you start on the trade screen and the Pokémon are right there, waiting.
And, just cause I'm on a roll, my PokéBank boxes are arranged as such: the first several boxes are full of 'close but not quite' Pokémon from breeding. They either have the wrong ability or fall just short of the right IV spread but either way, unfortunately they didn't make the cut for my team. However, all of them still have fantastic IV's and movesets, and don't deserve to just be released or Wonder-Traded immediately. These are the same Pokémon that are listed on my Trade Thread under the 'In Stock' section. They'll stay there until someone on my thread asks for them, at which point I retrieve them from Bank and trade them away, or until it becomes obvious that no one is really looking for that specific Pokémon at the time, and I Wonder Trade them to someone who will hopefully take care of them. Following these are several boxes that contain almost all of the Friend Safari Pokémon with their Hidden Abilities; after I get a new Friend Safari, I immediately go and catch a specimen, female if possible, of each Pokémon in that Safari with its Hidden Ability. They are then stored in one of the boxes in Bank until the are retrieved if/when I need them for an order. The Pokémon in these boxes are arranged according to type, with blank spots left for Pokémon that I haven't yet caught with their HA's according to Bulbapedia's list.
And that's how I organize and keep track of everything. I sorta went off on a tangent there, hope it was helpful, somehow...
