Out of the hundred and fifty or so mods I currently have running these are the few I can remember off the top of my head.
Before I begin, I'd like to recommend that you stay away from the Skyrim Nexus there are a lot of mods there that do have good quality however the vast majority are fairly unstable and commonly ruin saves.
You'll also need this for any major Skyrim Moddinghttp://skse.silverlock.org/Dogtown1 SkyMoMod://www.moddb.com/mods/skymomod-v12
Last time I checked there were +100 Monsters (All of them look really good or are modified from different games, no shitty monsters)
All of the monsters are added to the level list and only spawn in areas where they fit in or areas made specifically for them. (Some of them replace "Boss" monsters at certain areas.)
Towns and Villages Enhanced Collectionhttp://steamcommunity.com/sharedfiles/filedetails/?id=79384336If you're willing to take a slight hit in frame rate then this mod is awesome for adding new portions and extreme amounts of detail to almost every village and city in Skyrim.
Fair warning though, some towns lose the "Frozen" feeling to them with this mod, though that's not necessarily a bad thing
The Elder Scrolls Quest Serieshttp://steamcommunity.com/sharedfiles/filedetails/?id=16345I believe 5 of some of the best Quest mods made for Skyrim. Many of them have entirely new areas to them with their own environment and enemies. I'm aware that at least two of these have custom weapons and one of them has a custom companion.
The Asteriahttp://steamcommunity.com/sharedfiles/filedetails/?id=18628Before you go "That's to silly for Skyrim" apparently it's actually from The Elder Scrolls series and was used in one of the older games.
It a really cool house for stuffs and things so you should get that.
And my final recommendation before I go watch a movie.
SkyUIhttp://steamcommunity.com/sharedfiles/filedetails/?id=8122It fixes all of Skyrim UI so it's not ugly or mess anymore.
It also has a built in item search feature with Newest to Oldest items as an option.