http://www.skyrim.nexusmods.com/mods/37994/ has recently become an essential mod for me and many other users, with over 3000 endorsemants. The http://afkmods.iguanadons.net/index.php?/forum/345-unofficial-skyrim-patches/ are also essential mods for anyone with Skyrim on the PC. http://skyrim.nexusmods.com/mods/11163 and potentionally many other mods by http://skyrim.nexusmods.com/users/187943/?tb=mods&pUp=1 are also essential for myself and many others. I personally believe http://skyrim.nexusmods.com/users/2463371/?tb=mods&pUp=1 are essential for anyone's game, as they add to immersion in the game.
http://skyrim.nexusmods.com/mods/9557 Is something I'd also recommend, by http://skyrim.nexusmods.com/users/684492/?tb=mods&pUp=1, and many of his other mods.
http://skyrim.nexusmods.com/mods/19281 is also essential for me, as are the compatibility patches for other mods, such as http://skyrim.nexusmods.com/mods/38563/?. Personally I believe it is the most extensive and complete overhaul available, but it is very specific in it's changes and thus other mods svck as http://skyrim.nexusmods.com/mods/9286 and http://skyrim.nexusmods.com/mods/10037/? may be more fitting. http://skyrim.nexusmods.com/mods/24377//? is another mod that may potentially fit your taste and is becoming increasingly popular. Though out of Requiem, SkyRE, Ace and Combat remastered, you should only pick one. ACE is modular, so you have quite a bit of flexability with what features you want to use, and thus more compatible with big gameplay changers.
http://www.skyrim.nexusmods.com/mods/29624/ is a wonderful mod, extending the character creation process. Essential to my game, and without doubt, many others. http://skyrim.nexusmods.com/mods/12977/? adds quite alot of life to skyrim, and thus I also suggest it.
I also suggest http://skyrim.nexusmods.com/mods/24913; this mod adds lots of new content without going OTT, adding content that is completely lore breaking. And if you choose to use Requiem, there is a http://skyrim.nexusmods.com/mods/36096/? for it too. I also suggest http://www.skyrim.nexusmods.com/users/258945 stuff too, some of which are replacers, others adding new content.
Those are some mods I can think off via the top of my hat; I've got over 190 mods installed on my game doing a wide variety of things.
EDIT:
Oh, and some essential tools for your game, if you choose to dive into modding it: http://skyrim.nexusmods.com/mods/6/?, http://skyrim.nexusmods.com/mods/25859/and http://skyrim.nexusmods.com/mods/1840/?.
Also ninja'd by alt3nity @ offical patches stuff. 