Randomness cheats

Followers Learning Spells
You can have your Follower learn how to use spells. Simply drop a Spell Tome Book, and tell your companion you want them to do something for you (Command mode). Have them pick up the books; they will now have learnt the Spells!
shout location and words of power
Here is a list of all the words for shouts currently available in the game, the locations of the words that are part of the shouts, if applicable.

Locations in bold are related to the main questline, and locations that are italicized are side quests, and underlined locations are Dragon lairs. Dragon Priest lairs will have "(DP)" listed in the quest section, after the quest listing (if there is one)

It will be listed like thus:

Word (Translation), Word (Translation), Word (Translation)

Location (Region) - Group: Quest Name (If applicable)

Some locations for Words of Power have more than one quest associated with them.

Animal Allegiance

Ran (Animal), Mir (Allegiance), Tah (Pack)

Angarvunde (The Rift) - Dungeon: Medresi Dran and the Wandering Dead
Ancient's Ascent (Falkreath Hold)
Ysgramor's Tomb (Winterhold) - Companions: Glory of the Dead

Aura Whisper

Laas (Life), Yah (Seek), Nir (Hunt)

Northwind Summit (The Rift)
Valthume (The Reach) - Dungeon/Dragon Priest: Evil is Waiting
Volunruud (The Pale) - Dark Brotherhood: The Silence has been Broken, Dungeon: Silenced Tongues

Become Ethereal

Feim (Fade), Zii (Spirit), Gron (Bind)

Ironbind Barrow (Winterhold)
Lost Valley Redoubt (The Reach)
Ustengrav (Hjaalmarch) - The Horn of Jurgen Windcaller

Call Dragon

Od (Snow), Ah (Hunter), Viing (Wing)

Main: The Fallen

Call of Valor

Hun (Hero), Kall (Champion), Zoor (Legend)

Main: End of Main Quest

Clear Skies

Lok (Sky), Vah (Spring), Koor (Summer)

Main: The Throat of the World

Disarm

Zun (Weapon), Haal (Hand), Viik (Defeat)

Eldersblood Peak (Hjaalmarch)
Silverdrift Lair (The Pale)
Snow Veil Sanctum (Winterhold) - Thieves: Speaking with Silence

Dismaying Shout

Faas (Fear), Ru (Run), Maar (Terror)

Dead Crone Rock (The Reach) - Daedric: Pieces of the Past
Labryrinthian (Hjaalmarch)
Lost Tongue Overlook (The Reach)

Dragonrend

Joor (Mortal), Zah (Finite), Frul (Temporary)

Main: Alduin's Bane

Elemental Fury

Su (Air), Grah (Battle), Dun (Grace)

Dragontooth Crater (The Reach)
Kilkreath Ruins (Haafingar) - Daedric: The Break of Dawn
Shriekwind Bastion

Fire Breath

Yol (Fire), Toor (Inferno), Shul (Sun)

Dustman's Cairn (Whiterun) - Companions: Proving Honor
Sunderstone Gorge (Falkreath)
Throat of the World (Whiterun) - Main: Throat of the World

Frost Breath

Fo (Frost), Krah (Cold), Diin (Freeze)

Bonestrewn Crest (Eastmarch)
Falgunthur (Hjaalmarch) - Side: Forbidden Legend
Skyborn Altar (Hjaalmarch)

Ice Form

Iiz (Ice), Slen (Flesh), Nus (Statue)

Frostmere Crypt (The Pale) - Dungeon: The Pale Lady
Mount Anthor (Winterhold)
Saarthal (Winterhold) - Winterhold College: Under Saarthal, Side: Forbidden Legend

Kyne's Peace

Kaan (Kyne), Drem (Peace), Ov (Trust)

Ragnvald (The Reach) - (DP)
Raanveig's Fast (Whiterun)
Shroud Hearth Barrow (The Rift) - Dungeon: Wilhelm's Scream

Marked For Death

Krii (Kill), Lun (Leech), Aus (Suffer)

Autumnwatch Tower (The Rift)
Dark Brotherhood Sanctuary (Falkreath)
Forsaken Cave (The Pale) - Side: The White Phial

Massive Smithing Leveling
You need around 1000 Gold for this. Simply go to any Smith selling Iron Ingots and Leather Strips. The first building on the right as you enter Whiterun is best for this. Purchase as many Iron Ingots as you can and equal Leather Strips. Then go and build as many Iron Daggers as you can. You will increase your Smithing Skill by 1 for every dagger you make. This can mean levelling your skill up by as many as 20 points in under 10 seconds! Then, sell the Daggers to back, and repeat with the money you have remaining. Whilst you aren't going to be able to do this for unlimited times (as the store will run out of Ingots/Strips eventually and you don't gain as much profit from the sell-back, it is a great tactic to very quickly level up your skills.
More Inventory Space
It may be easy to forget/overlook, but increasing your stamina with every level up also increases your weight carrying capacity by 5.

Skyrim's Refresh, Respawn and Restock Durations
As with previous Bethesda games, certain things such as harvested items, stores, containers and enemy spawns, will 'refresh' at certain intervals. Stores will take roughly 2 to 3 days to restock their goods and gold, whilst previously cleared areas of enemies take roughly 3 to 5 days.

Verified by: this cheat is unverified
Standing Stones - Info and Locations
Stone - Information - Location

Skill Improvement Stones
Warrior Stone - Combat Skills increase 20% faster - The Guardian Stones (Falkreath Hold)
Thief Stone - Stealth Skills increase 20% faster - The Guardian Stones (Falkreath Hold)
Mage Stone - Magic Skills increase 20% faster - The Guardian Stones (Falkreath Hold)
Lover Stone - All Skills increase 15% faster - The Reach

Other Stones
Apprentice Stone - Recover Magicka tiwce as fast; twice as vulnerable to magic - Hjaalmarch Hold
Atronach Stone - 50 extra points of Magicka, 50% absorb spells, -50% Magicka Regen - Eastmarch Hold
Lady Stone - Regenerate Health and Stamina 20% faster - Falkreath Hold
Lord Stone - 50 points of Damage Resistance, 25% Magic Resistance - The Pale
Ritual Stone - Raises all dead around you to fight for you - Whiterun Hold
Serpent Stone - Paralyze the target for 5 seconds, and do 25 points of damage - Winterhold Hold
Shadow Stone - Invisibility for 60 seconds - The Rift
Steed Stone - Carry Weight +100, no movement penalty from armor - Haafingar Hold
Tower Stone - Unlock any Expert level lock (or lower) once per day - Winterhold Hold

Add Mercer
I was tired of Mercer Frey's attitude, so I thought the beginning of the Thieve's Guild quest "Speaking with Silence," would be the perfect time to kill him off. Turns out he's one of those NPC's you can't kill. After whooping him a few times, I ran far away enough that I could fast map out of the area. I went to White Run, and he came with me! Now he's following me everywhere, non-aggro to me and my first follower Belrand, and helping to kill other mobs! So now I have 2 followers although I can't gear him or give instructions. Still, he's a powerhouse with those two blades. It really puts the game on EZ mode, but after logging out and coming back in several times, running some quests, zoning around, and he's still there, I guess I'm stuck with him. I haven't gone to the Flagon to see if he can meet himself. I might have to go do that now...

Unbreakable Lockpick (Skeleton Key)
Submitted by pfc_shadow
During the quest "Darkness Returns," part of the Thieves Guild quests in Riften you'll get a quest item called the Skeleton Key, a lockpick that cant be broken. Instead of finishing the quest you can just keep and use it to open any door or chest without worrying about running out of Lockpicks.

Easy 100 Restoration Skill
Submitted by g-rayted
You need 2 spells for this: Equilibrium and any healing spell (preferably Fast Healing or better). Cast Equilibrium which drains health for magic and keep healing yourself. You will constantly lose health and never run out of magic so you can heal yourself forever.

Easy 100 Speech Skill
Submitted by rbradner
Travel to Riften and go to the Black Brier Meadery. Talk to Ungrien at the front desk and ask him about Maven Black-Brier. He'll say something nice. You now have the option of persuading him, bribing him, or just accepting what he said. The persuade has a Speech check of 25 (must have 25 Speech to get it). If you don't have 25 Speech, try the bribe. It will up your speech rather quickly to 25. Once there, you can use the persuade repeatedly to get to 100 Speech (or however high you want it).
Just keep asking about Maven and persuading. It took me about half an hour tapping the A button while I watched TV to get to 100.

Walk Faster While Over-Encumbered
Submitted by kcrobxer
When you are over-encumbered, you can move faster by equipping a bow and drawing an arrow back.
Combine this with the perk to walk at normal speed with an arrow cocked and you can move about like normal.