I like to use:
Advanced Filters – adds skyrim like filters to your inventory and bank spaces. makes organising much better.
Foundry Tactical Combat – for floating damage, improved character & group windows, buff/debuff displays, dps tracker.
Item Saver – adds a star next to items as a visual reminder to not sell / deconstruct
pChat – I use this mainly for the timestamp but it has other useful functions.
Wykyyd’s addons – particularly toolbar, quest tracker, achievement tracker, outfitter. Toolbar is great to be able to see info at a glance (highly customisable), outfitter is amazing so you can quickly swap skills and gear (e.g. pve and pvp sets)
even using all these mods (see the general mod page, crafting & discovery mods) my screen is still fairly uncluttered and minimal (especially for an MMO) The chat tab disappears if no one is chatting, the quest tracker can be expanded and the achievement can either track achievements by zone automatically or you can just track the ones you choose.