whenever i'm loading up an old save from an old character, the first thing i look at is the hotkey set-up,
it gives me a lot of info about what i was up to with that character at that particular stage, how i played,

this probably works differently for pc users, but on a console you get 8 keys, on the d-pad, so 4 mains, which are easy to hit, and 4 corners, which are a bit more awkward,
so usually the important ones go on the mains, or the ones you need in a panic, and the leisurely ones on the corners, that's the general idea anyway,

and overall what i try to get with the hotkeys is a smooth game, for me its a means of avoiding pause, both inside of combat and out, but yeah...

my current loadout, clockwise from the top, is as follows -

mains - Bound War Axe / Steel Bow / Eye of Night / Calm
corners - Damage Health Poison / Boots of the Shark / Mortar and Pestle / War Cry

so, let's hear some others...

Mine changes for every character, but I've only ever used all 8 on my mage, and it was as follows:

Up - Restore Health
Up/Right - Detect Life Hood
Right - Shock Damage
Bottom/Right - Summon Lich
Bottom - Drain Health, Weakness to Magic
Bottom/Left - Invisibility or sometimes Fire Shield
Left - Summon Dremora Lord
Up/Left - Fire Damage.

The only thing that stays constant between my characters is that up = restore health for mages, repair hammers for warriors, poisons for thieves.

PC here. The character is a mystic archer. No weapon is hot keyed because she only carries one - a bow.

1. Invisibility.
2. Summon clannfear and go invisible.
3. Absorb health on touch (mostly for underwater fighting).
4. Free - it changes depending on the environment.
5. Utility. This can range from charm to open lock to keying a night eye ring.
6. Demoralize (changes to turn undead if appropriate).
7. Command Creature (changes to command humanoid if appropriate).
8. Combo prep spell: Drain speed + Weakness to poison + Soul trap .

Only use four,
ranged aoe destruction spell
on touch destruction spell
repair hammer
restore health and fatigue,
but tend to make new spells to replace them every one or two levels.

I'm on PC and use the STHotkeys mod, which let's you assign multiple items to the same key and cycle through them, so I tend to use the keys for broad categories of things rather than specific things.

1: Azura's Star
2: Weapons, or primary offensive spells for mages.
3: Secondary spells - depends on the character. These tend to be secondary offensive spells.
4: More spells - again depends on the character. These tend to be utility spells - conjuration and illusion mostly.
5: Light or Night-Eye, whether a spell or an enchanted item
6: Repair hammers
7: Alteration - generally feather and shield
8: Healing spell

I'm on PC, and using the WASD movement keys, so I tend to assign keys 1 through 4 to my most quickly needed items.

Because I alternate among several different character types, I use those keys in a semi-consistent way

1 is always my primary weapon. That would be my big enchanted sword, if I'm a warrior, or it would be my primary summon, if I'm a conjurer. When I push it, I know I'm ready to deal with whatever is presently running towards me.

2 is always a ranged weapon. It's my bow if I'm any sort of fighter, and it's a ranged destruction spell if I'm a mage.

3 is almost always allocated specifically to an Absorb Health effect, assuming my character uses that (most do.) It's right at my index finger, and I can remove health from the enemy in front of me and give it to myself.

4 is my secondary weapon slot. For fighters, that's usually a weapon enchanted with soul trap, to fill soul gems for my main weapon. For a mage, I often put Paralyze on that key. Sometimes I use it to key up a shield spell.

5 and 6 are still reachable with my index finger. 5 is often Dispel for mages. 6 is almost always assigned to healing potions. 7 and 8 are my "open" keys, for whatever the character needs handy.

1 - Healing spell
2 - Ranged multi-effect Destruction spell
3 - Nasty ranged Fire spell
4 - Nasty ranged Shock spell
5 - Summoning spell of choice (varies)

6, 7 and 8 are situational. Turn Undead for undead or necro dungeons, Frenzy/Command Humanoid for NPC enemies, Invisibility/Chameleon also for NPC enemies. I certainly do love me some Destruction magic, but clearing NPC dungeons without being detected (unless I'm Commanding someone) or doing any direct damage is something I enjoy too.

For Lothran it differs depending on whether he′s in Bruma or elsewhere. But I′m gonna go with his summer setting, which I think I know what it′s gonna be this time.

1. His always-carry item, the Dark Dagger (this one never changes)
2. Main weapon, usually a sword
3. His enchanted bow
4. The spell that goes with the bow
5. Absorb health
6. Various attack (or immobilize) spell
7. Shield
8. Restoration

1. Changes depending on character and situation
2. Summon
3. Healing
4. Shield
5. Detect
6. Touch Spell
7. Range Spell
8. Repair Hammers (I hate digging down through the menus)

360 here:

Up: Destruction Touch Spell, kills nearly all, this is the emergency spell
Up/Right: Azura's Star
Right: Repair Hammers
Right/Down: Custom Summon Clannfear Spell (longer than normal spell)
Down: Enchanted Bow
Left/Down: Custom Destruction Ranged Spell
Left: Custom Destruction/Turn Undead Spell
Left/Up: Enchanted Daedric Short Sword

1. Torch
2. Repair Hammer
3. Whatever spell is most relevant, whether it be a Destruction or Conjuration spell or something else
4. Restoration spell of whatever level is most useful
5. Actors In Charge orb, from a mod that allows me to do any vanilla animation
6. Actors In Madness orb, from a mod that allows me to do any SI animation

7-9 are usually unused.

My hotkey setup depends on the character I'm playing. My main character is a Recon Sniper named Elberond that uses Marksman (big shock, I know ), Illusion, Conjuration and Alchemy. The setup:

1. Main bow (not enchanted)
2. Secondary bow (enchanted)
3. Illusion spell (depends on what he's doing)
4. Conjuration spell + Invisibility (used for combat assistance, distraction and sometimes escape)
5. Variable (changes with the situation)
6. Alchemy gear (so he can make a potion or poison at a moments notice)
7. Summon/Command mount (mod)
8. Repair Hammer

Bow / Chillrend / Custom Poison / Shadowrend / Wizards Fury / Cowl of Nocturnal

On my current most played character it goes like this:
Top: Restore Health
Top Right: Azura's Star
Right: Bow
Bottom Right: Combo Elemental Damage Spell
Bottom: Light Spell
Bottom Left: Combo absorb health/magicka/fatigue spell (on touch)
Left: Sword
Top Left: Repair Hammer

I really like this setup because it allows me to almost never have to pause (I don't use potions very often). It will probably change once he gets to a higher level though. For instance, he can't effectively use silence or paralyze yet, but once he gets illusion up a combo paralyze/silence spell will most likely make its way onto the hotkey wheel. Azura's Star and Repair Hammer always get top left and right respectively on every character. The healing method of the character is always at the top. Using two weapons all the time makes hotkeying kind of difficult because each weapon needs its own main hotkey. Since destruction is not one of my majors what will probably end up happening for my final wheel is light will go to bottom left, super combo absorb spell will go bottom, and super combo elemental damage/paralyze/silence spell will go bottom right.