There are many many many good mods out there. Take at look at the
top files on the nexus. I recommend getting the nexus mod manager, makes modding really easy. It comes with an automatic downloader, mod categories, plugin list, archive invalidation and much more. You should also take a look at
BOSS it takes care of the load order of your mods for you (very important to avoid conflicts). You will also probably want a leveled list merger (allows you to have many mods which changes the leveled list (list of loot) together), I recommend ASIS, see below.
Some of my personal favorite mods:
Kagrenacs Instant Fortress : A fortress you can deploy anywhere you want in skyrim, a ring that teleports you (and your followers) directly to the fortress and back to the point you were when you used it, plus the ability to send followers you dismiss to the fortress. Spouses can move there (they WILL sleep in your bed). Tons of storage, display racks, mannequins, everything you could possibly need.
Convenient Horses : Horse combat, horse armor, horse following, horses for followers, horse inventory, ability to pick ingredients from horse back, horse stat and behavioral tweaking etc...
Dual Wield Parrying : Allows you to parry while dual wielding or with weapon + spell and even in fistfights.
Ultimate Follower Overhaul : Follower limit increased to 15, change full inventory, make follower able to use spell books, show stats, toggle essential or not, group commands, no level caps etc...
Mighty Magic : Modular. Spell scales to skill in appropriate school. Decrease spell cost replaced with increased magnitude, for enchanting and potions. Adds new spells, balances the spells found in the game. Balances the mechanics, stagger for example, and much more.
Midas Magic : Adds tons of cool and balanced new spells.
ASIS : Adds potion and healing for npcs, increased spawns, leveled list merging, smarter enemies, npcs have perks, spawn randomization and a lot more.
Climates of Tamriel : Overhauls the weather/climate system, adds tons of new weather, region appropriate weather, atmospheric conditions, thunder, realistic lighting etc...
Skyui : Reworks the interface to make it a lot more pc friendly with many new features, such as sortable columns, colored icons, configurable text size, full text search, efficient keyboard navigation etc.
Categorized Favorite Menu : Adds categories to the favorite menu and it now takes the whole screen.
STEP : Tons of graphic improvements.
SKSE : Some of the mods above work better with it (see the individual description of each mod), although it is Optional.
ENB : Graphic *system*, makes skyrim look a lot better, for lack of better words. If you use it with SKSE above, you need to use the dll, unless it changed.
Of course all those mods are compatible with each other.
There's also tons of graphic improvements (many that don't decrease peformance) which I won't mention here.
You can also take a look at the
quest and adventures category on the nexus, there's tons of mods that adds many dozens of hours of gameplay to skyrim.
If you want I could post my whole mod list.
If you need any help, I will be following this thread.
EDIT: typos