It will vary greatly depending on who you ask (or who replies). I recommend checking out www.esoui.com for anything that sounds interesting (or searching for addons you find yourself wanting).

But I'll recommend some too: I like the minimalist UI so I'm trying to avoid adding too much to it, and making sure they blend in seamlessly - ideally a new player should look at my screen and be unable to guess what's an addon and what's original.

Binder & Unified Chat Tabs
IMO These are must have addons if you have a lot of alts (or even play more than 1 character). Binder lets you save key bindings and load them on any character, and Unified Chat Tabs does the same for chat tabs and colours. It saves so much time when I make a new character. Neither of them adds anything to the UI, so when you're not using them to save/load settings you'll never know they're there.

Azurah
This lets you move all parts of the original UI around the screen (recently updated with new options after I complained on the forum) and has options to add some extra info like numerical values for your health, magicka, stamina and XP and Ultimate amount in a relatively non-obstructive way. (And there's options to turn each part on/off individually.)

Srendarr
Adds buff/debuff trackers. There are a lot of addons that do this, but this one is my personal favourite. Mainly because I feel like it blends in with the original UI extremely well and it's highly customisable. I have my buffs/debuffs as little icons on either side of my action bar and my targets next to their health bar.

Advanced Filters
I only got this one yesterday but I already love it. It adds a row to the inventory and bank that lets you sort your items by sub categories, for example showing only medium armor (or even medium helms below level 10).

Mini Map
This is easily my most overt addon, but I love it. I have a terrible sense of direction so the compass just isn't enough for me. I was constantly having to stop and check my map and now I can do it while moving.

This is a great thread where this topic was recently brought up (with up-to-date info)>

http://forums.elderscrollsonline.com/en/discussion/156849/recently-released-add-ons-that-are-amazing-and-must-haves

[Edit]: And just for reference: I PVP a lot so I try to keep my addon load low; I really only use "foundry tactical combat" when I am in cyrodiil. Things like "master merchant" I'll drop into my addon folder when I want to sell a bunch of stuff (about once a week), then will copy and paste the library and delete the file from my addon folder when done (I think this is excessive though, I can be a little... funny ).