There are a plethora of mods being uploaded for Skyrim players on all platforms, many have yet to be perfected while a select few can revitalize the entire experience. From additional perks, to the addition of massive battles related to the civil war, all the way to completely new followers and ways in which to interact with your companions; not to mention mods that add entirely new weapons and armor to the mix.
First and foremost comes one mod that has singlehandedly enhanced the Skyrim experience more than any other mod I've come across.
Ordinator-Perks of Skyrim, Authored by EnaiSiaion.
Bringing more than 400 completely new and revamped perks into the fold allows for a revolutionized ability for character customization both in and out of battle. Combining heavy and light melee attacks can create for increasingly deadly results, while Heavily armored soldiers can also drop a selected standard which boosts the defenses of nearby allies. Stealth oriented characters can set tripwires, activate smoke clouds, or drop exploding mead barrels upon executing a dodge roll. Last but not least mages can expect to conjure a near endless army of the undead, teleportation is introduced, and even the ability to potentially damage enemies using healing spells!
Isilmeriel's LOTR Weapons allows players to take up everything from Aragorn's Narsil (eventually upgradeable to Anduril,) to Frodo/Bilbo's Sting, right down to Sauron's mace and various Wraith/Witch King blades. There's also Legolas' short-blades as well as an Elven Longbow which can further add to one's roleplaying. Not only do these weapons look fantastic they also can deal some truly devastating blows. It's worth noting that there are currently mods authored by JPDocter which individually add Legolas, Gimli, Aragon (as Strider) and even Gandalf although their voices don't really fit and not all their appearances are up to par.
Apocalypse - Magic of Skyrim is yet another mod authored by EnaiSiaion, with 155 new spells (31 per school of magicka) this mod takes the Vanilla spells and makes them look like child's play. Even after countless days upon days of playing it's safe to say I have barely scratched the surface of all the newly added spells herein. Everything from molten rocks that do more damage as they travel further, to using alteration spells to fabricate beds, bridges or teleporting milestones, right down to healing relative to how much damage a given marked target receives.
Wet and Cold by Isoku is yet another revolutionary mod which adds several layers to the games aesthics. Craft yourself a backpack which actually displays certain items like torches and woodcutting axes if they're in your inventory, equip various cloaks to combat different types of weather. You'll even notice actors will have visible breath in frigid temperatures while also being able to actually see snow resting on one's gear etc.
Last but not least comes 'anotha one' from Enaisiaion in the form of Imperious - Races of Skyrim. Whereas vanilla Skyrim offers an incredibly unbalanced set of different racial abilities both active and passive, this mod asks to level the playing field while also revitalizing different playstyles. Dark Elves will hear ancestral whispers which mark random targets for death while Redguards have unlimited stamina outside of combat, this mod adds multiple effects and abilities to each of the various races and creates for a much more balanced selection.