I'm one of those people that likes to have as many open spaces as possible on my hotbar so that I can quickly access what I'm using on my current project - so I keep nothing in my hotbar! I keep 9 essential items in my inventory on the right so that I can shift-click them into my hotbar if necessary.
These items are:
-Arrow (for Infinity bows)
-Punch 2 and Infinity bow (for elytra flight)
-Bow with Infinity, Punch, Power, and Flame
-A few ender chests
-Silk touch pickaxe with Mending
-Sword with Knockback, Fire Aspect, Looting, and Sharpness
(yes, I have these in alphabetical order)
I keep food in my offhand (porkchops or steak) and of course have an elytra equipped along with armor.
The reason I have ender chests is because I use them as a backpack with some items that I will probably need but I won't need as much as the items I keep in my inventory.
These items are:
-Chestplate (for when I don't need my elytra equipped)
-More food and torches
-Boat (for transport, since there are rivers near my base)
I also like to keep my ender chest clutter-free so that I can put more building materials in there.
EDIT: I totally forgot wood, I keep a stack of planks in my ender chest at all times.
The left end of my hotbar stays fairly standard during most of my play sessions: 1-Sword, 2-Pick, 3-Main Bow, 4-Food. 5 is where I put my fishing rod when using an AFK fishery, but otherwise ends up being an axe; 6 is often my shovel, except when I put my axe away in which case I put my shovel right next to it; 7 is my Engine Bow, for elytra boosting; and 8 and 9 are free for whatever I need. I typically keep my elytra equipped at all times, with Mending diamond gear in every other slot, and I keep a Mending diamond chestplate in the upper right corner of my inventory. I also have an arrow positioned directly above my bow, and go to great lengths to ensure that other arrows don't stack with it (I really should just rename it).
1. Pickaxe (Fortune III, Unbreaking III, Efficiency V, and Mending).
2. Bow (Power V, Flame, Infinity, Punch I, Unbreaking III and Mending).
3. Sword (Sharpness V, Sweeping Edge III, Looting III, Knockback I, Unbreaking III and Mending).
4. Axe (Efficiency IV, Silk Touch, Unbreaking III and Mending).
5. ... situation specific item (or empty).
6. ... situation specific item (or empty).
7. Building block (cobble, or whatever is plentiful).
When I am actively hunting mobs I swap my bow to the offhand and hold my looting sword in my main hand. That allows me to attack with either, while giving me the looting bonus for the bow as well. And since the shield is right next to my sword (in slot 2 where the bow was), I can easily switch to the shield to block.
When mining I will have torches in my offhand.
In my early days of Minecraft I settled on this layout and have been using it since then. Before the offhand was available it allowed me to easily switch between pickaxe and torches while mining with just a single mouse wheel movement, and to food or weapons with no more than a two slot turn.
I usually do it compulsively i.e without putting much thought into it, I just do it when I have a chance and will need a specific item. Usually it goes like 1: Sword 2: Bow 3: Pickaxe 4: Food 5: Blocks 6, 7, 8 and 9 usually whatever else I may be carrying that is useful at the time.
It has been over two years since I posted in this thread but I still organize my inventory almost exactly the same way, the only difference being that I now trade for diamond gear for repairing so I no longer reserve a slot for diamonds in my Ender chest and instead use a slot or two for those items (when playing vanilla; modded is virtually the same except diamond is replaced with amethyst).
1. A Sword, so I can slay mobs at a moment's notice
2. A Pickaxe, for my frequent mining adventures. I used to have it in the first slot, until I started playing Voxelgarden and Tinker's Construct, which gave a pragmatic case for placing a pickaxe directly to the left of my torches.
3. Torches, for lighting up mines and placing navigational markers. Sometimes, when I need to place a lot of torches for spelunking in 1.9+, I have my sheld here instead.
4. Miscellaneous, sometimes a bow, but I'm mostly a melee fighter.
5. Miscellaneous, sometimes a compass to help me find my way home more efficiently, or a clock because I'm too lazy to look up at the sky.
6. Miscellaneous, sometimes a crafting table for convenience.
7. A Water bucket, to make crossing lava lakes less dangerous. It's placed in a distant slot to prevent me from using it accidentally.
8. Food, because... well... I get hungry!
9. Cobble, for pillars, bridges, emergency bunkers, etc...
I also consistently keep reserved slots for logs, planks, sticks, and coal, in that order. In 1.8 and below, they are arranged starting at the top left corner and moving to the right. In 1.9+, they are placed on the opposite side and moving to the left, so they are closer to the player crafting grid and the off-hand slot.