This is my UI as of patch 5.3. I'm constantly tweaking/filtering out/adding new stuff as needed, so if you see something in action that isn't listed here, feel free to ask about it!
LUI - The base package for my user interface is LUI. I have naturally readjusted a few things, such as opting out of the standard raid frames for Healbot and changing my damage meter, but my unit frames and the general look are all LUI. A few things that I love outside of the look of LUI: the sliding side bars (marked as 1 on the right, there's also a hide-away bar closed on the left) and the ability to hover over Guild and Friends (top right hand side) and see who is online via drop down list. Also gives the ability to fade out chat/Omen/Recount (which I do not have enabled, see Skada), which is a neat aesthetic.
Addons that come with the LUI package:
Bartender4 - Button placement.
ButtonFacade - Makes buttons pretty.
Grid - Disabled and replaced by Healbot.
Omen - To the right of the chatbox.
Recount - To the left of my raid frames.
Embedded oUF - Background stuff that makes LUI work.
1) ForeXorcist - I get asked about this addon a LOT. This FX is both my cooldown slider bar and my DoTimer. It can track pretty much every thing; DoTs, internal proc cooldowns, ability cooldowns, you name it. Unfortunately it hasn't been updated in a long time, therefor it's pretty buggy. I've actually tried disabling the cooldown slider all together, simply because it's information that I rarely use, but it won't stay off. FX is a huge use at your own risk addon, one that may very well be completely broke come patch 5.4. If it does break, I'm going to be really sad, especially since FX has plugins for LUI so everything looks all nice.
2) Deadly Boss Mods - Your standard boss mod. I personally prefer DBM over BigWigs, but this is preference simply because I've been using DBM since I started raiding all of those many years ago.
3) MikScrollingBattleText - This addon creates a lot of text on a screen that may or may not be actually useful to you unless you use Fraps and watch the numbers roll in. I like to use this spam as quick references. I'm constantly filtering/tweaking/readjusting the position of MSBT to try and get the most out of all the information it provides. I'll probably also filter out the incoming panel in the near future, as I really only care about the outgoing damage I do these days.
4) NugComboBar - A great addon to help any class that has a combo point or stacking combo point system, which is to say nearly everyone. It tracks Maelstrom procs, feral combo points, rogue combo points, hunter pet focus, holy power, Soul Shards, Shadow Orbs, as well as quite a few other abilities that seem to be escaping me at the moment.
5) TotemTimers - This addon offers up a lot of different tracking for shaman, but I really only use it for its namesake: totem timers. I like that it shows me how long a totem has left and when it'll be up again, even though the latter is duplicate information for me.
6) ShieldsUp - I originally picked this addon up during Heroic Spine of Deathwing progression to help me track my Water Shield. With the changes to both Water and Lightning Shields (they're now both constant buffs that just need to be refreshed after a death/once an hour) you'd think that this addon would have become useless. Wrong! I still use Shields Up to keep track of the number of Earth Shield charges I have on a target as Restoration and it will also track the number of Fulmination stacks I have as Elemental. It's sometimes also a nice glaring reminder that I don't have Lightning Shield on as Enhancement, in the odd event that I forget about it or had been recently MC'd during an encounter and the boss gave me Water shield.
7) TimeToDie - A great addon to help you gauge whether or not your raid's current dps output will be able to beat that 3/5/whatever minute enrage timer.
8) Error Monster - Notice a certain lack of "That ability isn't ready yet." spam at the top of my screen? Yup, that's Error Monster. It filters out both the visual and audio spam that can occur during a fight. You can set up the filters to whatever extreme you prefer, but I've pretty well just filtered out all of it to help clean up an already chaotic visual/audio interface.
9) Healbot - My preferred healing mod that I've been using since The Burning Crusade. I've been sorely tempted to swap to Vuhdo a few times, but just as I'm about to finally take the dive, HB releases a fix to whatever major bug it was having.
10) Quartz - Unfortunately my screen shots do not show Quartz in action. I don't often hardcast as Enhance, and when I do it's usually pretty quick cast anyways, so you can't see where my cast bar is on the initial shot. I also apparently didn't time the shot when Durumu was channeling anything, so you can't see the enemy cast bar either. Each bar hangs out slightly beneath their respected unit frames; my cast bar is just a bit below my unit frame, my target's below their unit frame.
In this shot you can see where my various bars lay with Bartender. The box on the right-ish side of the screen is where my Naga mouse bindings hang out, which has been made to be fade out at all times and invisible/click through during combat. You can easily see where both my right and left hide-away bars are located. My extra-almost-never-used-buttons, extra mounts, and professions clusters all hide until I mouse over them to help clear up screen space. Bartender pretty much makes my life as an engineering shaman tolerable. So many damn buttons...
Addons you may or may not notice.
Button Facade (now Masque apparently) + Darion - Just makes my buttons a bit prettier, as well as helps to make them stand out a bit more.
Tidy Plates - Love Tidy Plates. Seems to make clicking on a target a bit easier and makes things look a bit less chaotic with multiple nameplates than the standard ui does.
Quality of game play addons.
ArkInventory - I began using this addon prior to the implement of the search feature into the standard UI. This addon not only turns all of your bags into one giant bag, but allows you to search all of your alts simultaneously for a certain item, view an alt's bags, and will restack/sort all of your items if you tell it to, plus more! Super handy addon to have, though a bit heavy. There are alternatives out there that run a bit lighter, but ArkInventory is my personal favorite.
Bags and Bank (Post Void Storage)
Disabled ArkInventory for the Guild Bank
Mapster - Turns my giant map into a smaller one that can be pulled up while still being able to see.
Mapster + NPC_Scan Overylay
_NPCScan - As many of you have guessed by now, I am a hunter of rares. I would have missed many a kill and tame if it wasn't for this addon and its counterpart, _NPCScan Overlay.
Atlas Loot - For all those data base search needs. Lists loot of every boss in the game, craftable items, tier sets, tabards, and so much more.
clsaver - Automatically enables combat logging when you enter a raid instance while in a raid party.
Postal - Allows select and mass looting of your mailbox.
Bug Grabber + Bug Sack - Catches errors, records them, and helps to prevent a lot of LUA spam.