Well, graphics stuff I've got are;
"Climates of Tamriel" (A mod that adds more weather effects and the like),
"Footprints" (adds footprints when walking in the snow and ash.).
"Inconsequential NPCs" (recommended to me by someone here a few pages back. Adds random, no purpose NPCs to towns to act as filler)
"Realistic Lighting Overhaul" (Though only the exterior and dungeon parts. I found it made inside of houses far too dark. I'm more accepting of having to use a torch inside dungeons)
"Water 2.1" (changes water in the game as well as adding waves to the coast and effects to rivers for flow direction)
"Wet and Cold" (adds some effects like blizzards slowing you down, NPCs wearing hoods while it's raining, backpacks, cloaks and hoods etc)
"A Quality World Map" (adds visible roads to the world map. I believe it can also add territory boundaries).
Other than that there's;
"Moonlight Tales" (Werewolf mod. I got it because I wanted being a werewolf to be a bigger inconvenience. It has forced transformation on full moons as well as a small chance every night. Also a number of new skins and eye colours),
"Werewolf Perks Extended" (adds a few more perks to the Dawnguard tree; more claw damage, stronger howls etc),
"Better Vampires" (changes things for vampires. I haven't actually had a vampire character yet so I haven't seen the effects of the mod),
"Better Fast Travel" (not so much better as more restrictive. Removes map fast travel and adds carts to towns and villages and boats at coastal areas),
"Civil War Overhaul" (adds more events with the civil war quest line. Apparently it's stuff that wasn't finished in time for Skyrims release),
"Cutting Room Floor" (adds a few NPCs that weren't included, as well as a few dialogues that never occurred in the base game).
"Immersive Armours" (not really immersive as much as it adds a bunch of new armours with crafting functionality.
"Immersive Weapons" (same as above. Includes some weapons from Morrowind).
"Moonpath to Elsweyr" (mod that takes place in Elsweyr. Only briefly looked into it with a character that was too weak to survive. Level 10 or higher from what I saw.)
"Daedric Lord Armour" (Adds the Daedric armour from Morrowind to Skyrim. Craftable and also includes the Face of Inspiration and Face of Terror masks. This is awesome to behold and probably my favourite mod despite its simplicity.
"Requiem" (I'm trying this one out now. It greatly changes how Skyrim is played. Removes levelled creatures and loot rewards, combat is very deadly with no health regeneration, some perks require you to read books before they can be gained or to have certain ingredients in your inventory, stamina drains while running and also if you're wearing heavy armour and don't have the first perk in the heavy armour tree. You'll need to take your time with it and I don't really recommend it for a first playthrough. Enjoy Skyrim as an action RPG first than maybe move to this but I recommend reading through the manual PDF first to understand the new mechanics.
There's also "SkyUI" (changes the user interface to a more PC usable one) and "SKSE" (A script extender). Both of these are needed by most of the mods listed by me here.
I also have the series of "Unofficial X Patch" mods. Bug fixes for the base game and DLC. There was a mod I used called "Character Creation Overhaul" that gave race bonuses and permanent birth signs but I disabled it because it wouldn't have worked with "Requiem".
I did download a mod called "Skyrim Flora Overhaul" and, while it looked nice with the trees and such, I ended up uninstalling it because it was too much for my computer. I have 4gb of RAM, Windows 7 32bit.
As of this moment, all these mods work fine together for me. I've only had a few crashes since I installed "Requiem" and I'm guessing that's because of the larger amount of scripts running.
Any questions on these, feel free to ask and I'll try to answer as best as I can.