((I apologize for the lack of links. Later I'll update the post with links to each of the add-ons and some screenshots of my UI))
I use a lot of add-ons. A lot of them I forget I have and take for granted things they do. Like Prat 2.0 which is a chat box addon that lets me do a lot of things with my chat window that I take for granted, like link items in created channels, and scroll up and down with my mouse wheel. Speaking of linking items, I have one called Linkerator that allows me to link items by just typing the name in brackets (  ), even items that I've never obtained. It keeps track of items that I've seen on the Auction Hall, linked by other people and dropped in dungeons, even when I don't get that item, and items that I see in Cartographer dungeon maps with Atlas Loot.
Oh hey, there are two more great add-ons. Cartographer replaces your regular map with a customizable map you can change the size and transparency of, and make notes and markings on it. It also contains maps of Dungeons which is nice because the default map does not. Blizzard should really think about adding that themselves. Atlas lists loot for all of the dungeons and raids so you can see in game what might drop from that next boss.
Another one that is commonly used is Auctioneer which keeps track of the current market for items on the auction hall. I use this one on Frelon mostly since he's my bank alt now. He keeps track of the scans and puts all of my stuff up for auction that I need to sell with accurate pricing.
Recently I've been experimenting with Bartender3 and Ag UnitFrames. Using Bartender I got rid of the default action bars and replaced them with smaller bars all at the bottom of my screen. I did this for both Elionene and Salthier. I used the unit frames to put Salthier's frame and the target frame down near where the character is on the screen so I could keep better track of my health when tanking. So far it's been okay, but my main purpose was to make more of the screen for viewing the world, and less of it for the buttons and frames. I don't know that this saved me any space, so I may go back to the default soon. Honestly, what I could really use is a bigger screen. I'm currently using a little 13 inch macbook pro, and a bigger screen would give me lots more space to work with.
A wonderful add on, especially for Druids or any class with multiple gear sets, is the Outfitter add on. It basically let's you create an outfit and save it. Then you can switch to that outfit with a couple clicks or a button push, making changing clothes a breeze. It's even set to change automatically based on a setting. For instance, it will automatically put my tank gear on in bear form, and my dps gear when I switch to cat. Smooth. I don't know how I would function without it as a druid.
And then there's Titan Bar. I think this was my first add on. I really like having my bag space, ammo count, gold, experience numbers and latency information available at a quick glance on the bar. It also let's me adjust UI and Sound options at the click of a button. This is the first one I plan to update with the oncoming patch.
Of course, with Wrath looming on the not so far away horizon, add ons are quaking with fear. With any big patch, it usually takes a few days for the add on developers to update the code of the add on for the new patch. I can only imagine it's more so with a big patch like an expansion. Hopefully, a lot of the bugs can be worked out with the 3.0.1 update, and then when we actually install the expansion pack, it shouldn't be a big deal.