DBM aka Deadly Boss Mods: This addon will not only alert you to mechanics of bosses but alert those around you with chat warnings etc. Highly Recommended
Big Wigs: Same type of addon as DBM afaik but I don't use it. If you have DBM you don't need this.
GTFO: This addon will alert you with a loud beep/buzz if you're standing in any bad stuff on the ground. Highly Recommended
Angry Assignments: Easy to use notes that the Raid Leader can sync to you for different assignments in the raid. Although I don't believe this is necessary for normal/heroic EN, it may become mandatory in mythic.
Exorsus Raid Tools: This addon does so many things it would be hard to explain everything. If you're a healer I'd recommend this addon just for the raid cooldown tracker, it would be able to stop certain pandas from sniping your raid cooldown for example.
Power Auras: This addon can be very useful if there is a boss mechanic (debuff) or your/other class mechanic (buff) you need to be made of aware. This addon is for more advanced players.
Skada: Damage/healing meter that tracks much more than damage/healing.
Recount: Same as Skada, though in my experience the person who updates Skada is faster and more accurate.
OiLvL: Allows you to compare the ilvls of your group. Epeen stroking addon basically. But if youre feeling generous and see someone who rolled, and is a much lower ilvl than youself, you can easily know they need it more than you.
ElvUI: This addon is a total interface conversion. If you are tired of that same old drab wow interface that's been there for over 10 years get this and be refreshed. Highly customizable, not recommended for those of the tech/addon illiterate.
Dominoes: Dont want as big of an overhaul as ElvUI? This addon is for you. Allows you to customize the size and placement of your action bars.
Tidy Plates: The title says it all fixes all those enemies plates to make them easy to read and sort. Just as good for healers too when figuring out that sweet spot more people are standing for your Healing Rain or Efflorescence.
VuhDo: This is a great raid grid/interface addon that when properly set up can do wonders especially as a healer.
Gatherer: Tracks the location of any herb/mining node you've farmed since installation.
Personal Loot Helper: This addon will alert your party in chat automatically if someone gets an item in your mythic/heroic dungeon that is an upgrade for you or someone else in your party.
World Quest Tracker: Easy to use addon that tracks your world quests, even makes grouping to do world quests easier.
RareScanner: Scans for rares, although they are easy enough to find in legion. The only real use for this addon is for finding that ever elusive Time-Lost Proto-Drake in Northrend.
Handy Notes: This is a minor map addon that has many sub-addons for it, I recommend the LegionRares&Treasures. Linking to the search page.
AtlasLoot: Addon that cleans up loot tables for different raids/dungeons making it easier to find that piece with the right stats you want.
Disclaimer: I have not pvped since cataclysm. Im probably missing some new to market essential addons.
Healer Have to Die: Gives you a easy to click interface that allows you to find and destroy healers in Battlegrounds. Have you ever healed a BG? This addon is that reason you're at the graveyard. Essential for RBGs.
Battleground Targets: Similar to the HHTD except gives you a easy to click interface for all battleground players. Essential for RBGs.
Gladius: The arena version of battleground targets plus much, much more. If youre looking to go far, you must have and understand this addon.