I consider the following Skyrim mods essential:
SKSE: This expands Skyrims scripting language, allowing for more robust mods, most of the following mods will require it. It also incorporates the startup memory allocation patch.
Frostfall.
This mod takes Skyrim's renowned frigid climate and makes it a gameplay mechanic. Frostfall adds debuffs caused by exposure to the elements to the game, it's even possible to freeze to death if you're particularly stupid. It also adds many items and gameplay changes to help you survive, such as assigning exposure protection stats to clothing, portable tents and craftable campfires, and cloaks.
Climates Of Tamriel.
This mod adds new weather systems, textures, lighting, and several other effects. It's compatible with Frostfall, your character's exposure will change depending on the weather system.
Wet and Cold.
This adds weather related textures and effects. NPCs will equip gloves and hoods and take shelter in bad weather. Frostfall and COT compatible.
Cloaks of Skyrim and Winter is coming: Cloaks.
Adds many lore friendly capes and cloaks to the game.
Sounds of Skyrim; The Wilds, Dungeons, and Civilization.
Adds many new sound effects to Skyrim
Static mesh improvement mod.
This mod fixes some of the worst models and textures in the game. If you install no other graphics mod, install this one.
Immersive armors.
Adds many awesome and lore friendly armors to the game.
Immersive weapons.
Adds many awesome and lore friendly weapons to the game.
Immersive Creatures.
Adds many awesome and lore friendly creatures to the game. (though a few push the boundaries of lore friendliness)
Weapons of the Third Era.
Adds yet more weapons to the games.
Interesting NPCs.
This mod adds many new voice acted NPCs to the game, they all have extensive dialog trees and give the world a feeling of vitality that it was lacking before.