Plugins and mods
Dalamud plugins add features to Final Fantasy XIV while it runs. You install them from the Plugin Installer, which the /xlplugins chat command opens once the game is started through XIVLauncher.
Each plugin is built for one Dalamud API level. When Dalamud moves to a new level, plugins built for the previous one show (outdated) in the installer and stay off until their authors update them.
Mods from Nexus Mods replace the game’s models, textures and sounds on your own client and are loaded with Penumbra or TexTools.

Easily clean out your Glamour Dresser.

Automatically finely scales the game UI by resolution.
Save and load actions into hotbars without taking up extra job hotbars.
This is still mostly a dev tool for debugging, but people like it?

Push notify to your device when your duty is ready
Shows an overlay and/or sends alerts when your held currency items (or non-currency items) match configurable rules. A spiritual successor to CurrencyAlert.

Automatically rename your screenshots with character and location info.
Give your UI that premium, acrylic look upgrade. Because Eorzea looks better with some blur.
A classic arcade game.
Easily get general and role-specific hints in duties.
A mod that calculates what you can do with what you have.
Tobii and Eyeware Eye and Opentrack tracker support for FFXIV
For when you want to spend time fighting the boss, not fiddling with waymarks.
Keep on top of new items.
Total control over where to put your hotbar slots.
I'm ready, I was just alt tabbed!
Never think too hard about your bags again!

A simple utility that allows easy export of your gearsets to xivgear.app.
Get notified when someone enters or exits your mount!
That sure is a beeg dinosaur eat window.

Takes a screenshot upon death (and other events).

Add sender target name in chat messages.

Show how much damage your DoTs have dealt so far

A game to play when dead. A Puzzle Bobble clone mini-game.
Picks a random job!

Splits combos into more button for more button bloating. Requires BLU spells.
Client for the Archipelago Multiworld Randomizer.
Automatically copy ANY text on your screen by choice.
Parses Buffs to help understand what your party is doing.
Ever forget who you are? We can fix that!

Adds a quick special-symbol picker beside the chat mode button.
Lower 3D Resolution Scale

Changes your VO language on a per-duty basis
A Plugin that lets you add notes to item Tooltips

"See exactly where you stand."
Reminds you about retainer ventures.
View encounter strategy images.
See every item you and your party pick up, as it drops.
No more cringe during hunt trains. Temporarily filters away Shouts and Yells that don't contain a flag or an instance message.
Adds Moonbase Alpha TTS when in Cosmic Exploration. aeiou!