Despite The Elder Scrolls V: Skyrim being nearly a decade old with multiple patches and re-releases since it first debuted, there are still several glitches that exist in the game that can cause you to experience some unusual things. For example, Giant's clubs are powerful enough to launch the player into orbit and the Ice Form Shout used by the Greybeards causes an endless dance routine.
There are also several glitches that allow for some easier ways to play the game in general, with the majority of them being useful no matter what kind of character you want to play as. Some are helpful for a broad range of things, while others are very specific and are only beneficial for one or two things, but for the most part, all of these glitches are useful in some way.
Restoration Potion Glitch
By far the most well-known glitch in Skyrim is the Restoration Potion glitch, which helps many veteran players craft gear with ridiculous stats as well as power level several skills. The basis of this glitch is how the Fortify Restoration Potion interacts with gear enchantments, as all armor enchantments are classified as Restoration magic in the game, they are all buffed by a Fortify Restoration Potion.
Where this glitch comes into its own, however, is that these buffs can be applied permanently if certain criteria are met and it isn't hard to pull off. If your character has an Alchemy level of at least 40, the Benefactor perk in the Alchemy skill tree, and four pieces of armor with at least 8% Fortify Alchemy Enchantments on them, it is possible to create potions powerful enough to break the game.
After leveling up Alchemy through either a skill trainer or general gameplay and obtaining the gear items, craft a Fortify Restoration potion, which is most easily done with a Salt Pile and either an Abecean Longfin or Cyrodilic Spadetail, then enter the inventory menu. From here, consume the potion, unequip, then re-equip all of the items that have enchantments on them. For some reason, doing this will not only improve the base level of the enchantment but keep those improvements even after the potion should have worn off.
This glitch is very useful for power leveling the crafting skills, as you can create Fortify Smithing or Enchanting potions which have a percentage increase in the tens of thousands fairly quickly. However, it can also allow you to cast any spells for free or use infinite Shouts when combined with the Amulet of Talos.
Hidden Chests
One of the best glitches to take advantage of immediately after escaping the destruction of Helgen are the hidden chests found in a few places in Skyrim. For the most part, all vendor's inventories are contained within a chest found somewhere on the map, usually underground where the player can't reach without falling through the floor. There are two in particular, however, which are easily accessible to you and allow you to steal gear with strong enchantments or high-cost items such as Grand Soul Gems without repercussions.
One of these is found in Dawnstar, to the left of the mine entrance if you follow the main path all the way to the end. Hidden among the rocks, there is an invisible chest that links to the Khajiit caravan in Dawnstar and is a good way to quickly obtain weapon and armor enchantments since the Jarl's quarters are found very close by.
The second hidden chest, which is a little harder to find, is located southeast of Markarth. This chest is also linked to the Khajiit caravan and is found near where the caravan normally sets up if it is not already there. Behind the short stone wall to the right of the vendor, the hidden chest can be found just underground at the far end of the wall. As it can be a little harder to find than Dawnstar's, it is best to move slowly along the edge of the wall to find it.
Both of these chests can be looted whether or not the Khajiit caravan is actually present and will reset when their inventory does, meaning you can come back after a few in-game days to steal from their inventory again and again.
Baskets For Stealing
Although not necessarily a glitch, as an NPC's line of vision is linked directly to their eye models, it is something of an oversight on Bethesda's part that can be taken advantage of. This issue also gives the many, many baskets in the game an actual purpose, as their low value means they usually aren't even worth selling.
In any situation where you need to steal from someone but not pickpocket them, throwing a basket over their head will allow you to take whatever you want from around them, even if it counts as theft, with no repercussions at the time. The only thing you will have to worry about is when they eventually find out what you have done and send Hired Thugs after you, but as far as NPCs go, they generally aren't hard to defeat.
Oghma Infinium
This particular glitch only works in non-patched versions of Skyrim but allows you to infinitely level up every skill in the game without doing any work. To perform this glitch, you need to have completed Hermaeus Mora's quest and obtained the Oghma Infinium reward from the keeper of knowledge.
After completing the quest, instead of opening the book straight away, as this will cause the item to disappear, travel to the nearest bookshelf that you own and interact with it to place books on the shelf. After placing the Oghma Infinium on the shelf, exit out and interact with the book. For some reason, this will allow you to read the Oghma Infinium without it disappearing, meaning you can use it repeatedly to level up all skill trees in either the Warrior, Thief, or Mage set by 5.
For the most part, this glitch is nearly impossible to pull off on console versions of Skyrim, but can still be done on PCs with an older iteration of the game.
Monster Form Glitch
This glitch is a little hard to pull off but allows for some interesting things to be done such as equipping multiples of the same gear type at once. The main things you need to pull this glitch off are either the Werewolf or Vampire Lord transformations, though the Vampire Lord has the advantage of being able to be used multiple times a day without outside help, a companion that you don't mind potentially turning hostile, and multiple of the same gear item that appears in stacks, such as Divine Amulets or armor pieces.
With both a transformation power and a companion, find somewhere that no stray NPCs will see you, then transform and immediately talk to your companion afterward. If done correctly, you should be fully transformed while the dialogue screen is still up, as you can't normally talk to NPCs while transformed, and you should be able to access their inventory by requesting to trade items with them.
From here, give your companion the entire stack of gear items you want to equip at once, then equip them from their inventory instead of your own. For whatever reason, while in a transformed state, you can equip the entire stack at once rather than only one of each gear type, which is useful when using the likes of the Amulet of Talos for infinite Shouts, Amulet of Mara for infinite Restoration spells, or Amulet of Akatosh for vastly increased Magicka regeneration.