Mods that're really well integrated into the game, don't conflict with one another, and otherwise feel as if they should've been in the game by default. You can safely install all of these mods together, and they all fix problems with the game without feeling out of place. Not every mod I use is on this list--this is simply a list of subtle mods that improve gameplay experience without diverging or adding too much to the world.

A QUALITY MAP:
--Adds visible roads to the Skyim map. MUST HAVE!

BEGINNERS SHACK
--Gives a small, free and very simple form of player housing at the beginning of the game for safe storage.

DESTRUCTION OVERHAUL
--Makes Destruction magic viable for a pure-mage build.

FOLLOWER TRAP SAFETY
--Prevents your follower from setting off otherwise carefully-avoided traps.

HIGHER VISIBILITY ORE
--Makes ore much, much easier to spot.

JORRVASKR MAP MARKER
--Allows fast-travel to Jorvaskr, fantastic if you're a Companion.

LIGHTER POTIONS
--Changes vanilla potions' weight to 0.1, reducing their weight to 1/5 of their initial values.

MAP MARKERS: SHRINES AND TEMPLES
--A nice little mod that's self-explanatory; convenient and non-intrusive.

PICKPOCKET REWORKING
--Rebalances Pickpocketing to be much more usable, and removes the cap on success chances.

SMELTING PLUS
--Allows you to smelt useless weapons/armor into ingots.

STONES OF BARENZIAH QUEST MARKERS
--Exactly what it says on the tin.

THE PAARTHURNAX DELIMMA
--Lets you do the Blades quests without killing Paarthurnax.

WEREWOLF CORRECTION
--Adds Health Regen to Werewolf Form, and also removes the once-a-day restriction.