I spend most of my WoW time raiding and PvPing as a feral druid, and my interface is pretty complex (to say the least). Unlike Elizabeth, I often find patch day to be a complete nightmare! However, although I know I can make do without my truckload of addons, I find every one of them makes life a little easier. Here are some of my favourites:
Discord Action Bars make up the centrepiece of my UI. DAB's customisable keybindings are a lifesaver -- I have a hidden bar which maps the number pad to various ranks of healing spells, and another which enables shapeshift keybindings. I've also remapped F1-F12 to various macros, and allocated various other keys for quick access to mounting, weapon swapping and the like -- my G15 keyboard means that even Ctrl-Alt-M is just a single button away.
CT Raid Assist's presence is probably unsurprising given that I raid; I also use most of the other CTMod functions too, and the helper addon CTRA Tank Assist. Talking of tanking, TankPoints is pretty useful for putting together the best gear combination for tanking, and comparing with others. As well as CT's boss warnings, I also run BigWigs.
I'm a Titan Panel fan, and have found its at-a-glance information display very useful. I also use the Honor+ plugin, which tracks PvP achievements.
Got aggro? Titan Aggro is quite useful in helping you figure out where the aggro's going, and KLHThreatMeter shows a nice easy-to-understand relative aggro table which could save your skin.
Natur EnemyCastBar is more useful in PvP than PvE, though I've found it good for timing banishes and the like. Being able to see precisely what your enemy's up to, or when that ice block ends, is particularly useful -- especially if they're casting crowd control spells on you. I also use SpellAlert for nice easy alert messages.
Information overload? No such thing. Although I keep the regular player and target frames visible, I like having Drathal's HUD in the middle of my screen to show health and mana/rage/energy. Its combo point display is particularly nice. Also, despite the fact it's now built into the game, I still use Scrolling Combat Text. I'm used to it, and it displays overheal, which I find particularly useful.
Some other addons in the mix: coolDown, TrinketMenu, Outfitter, MobInfo-2, Druid Bar, Decursive, ClearFont, Auctioneer, SuperInspect.