Gamer Escape - Probably the most comprehensive wiki for the game. Tons and tons of info on basically everything, plus Discus comments at the bottom of each page.
ConsoleGames FFXIV Wiki - Another wiki, also very comprehensive, but in a more familiar, traditional, Wikipedia-esque format.
Final Fantasy Wiki - A good solid wiki, but has information for ALL Final Fantasy Games, so requires a bit of navigating.
FFXIV Guild - Somewhat out of date, but offers several still-useful guides for leveling things.
Garland Tools Database - Extremely comprehensive, constantly updated. Amazing for making lists of what you want and doing all the math for you on how to get it. Lots of other tools on the site, but this one’s the one you remember it for!
Teamcraft - Simliar in many ways to Garland, but has tools the above does not, and vice-versa. Requires a login, but also gives you access to community input, such as rotations people have figured out, as well as tracking your crafting and gathering logs.
XIV Angler - For when you need to know HOW to catch that @&$%ing fish. Baits, weathers, windows, even hooking info.
FFXIV Crafting Optimizer - Never lose mats to figuring out a rotation again! Also saves your stats in a cookie, so once you plug everything in, it’s easy to keep yourself up to date and come up with the best rotations. Also makes macros for you.
FFXIV Clock - Does exactly what it sounds like it does. For an alarm that will make noise regardless of what you’re tabbed into, use these settings.
Crafting as a Service - Find out what gear you need, find out what mats you need, and figure out how the HECK to level DoH.
Forum Thread - Desynthesis Guide - Exactly as advertised. Useful to get through items you can get from ARR and HW, but drops off there.
FFXIV Gardening - How to crossbreed, what to crossbreed, and what success rates you’re looking at. “Worth nothing that the efficiency ratings on FFXIV Gardening are NOT success rates! They are an efficiency calculation based on price of the seeds, how hard they are to obtain, and a few other factors.” Thank you @renofmanyalts for the clarification!
Ariyala Hunt Tracker - Ariyala has several other tools, but this is probably by and large the best dang tool on the site. It’s broken down by server, and it relies on peoples’ inputs for kill times. Of note, trackers for Behemoth, Odin, and Ixion are included.
Horus Hunts - Dedicated exclusively to tracking hunts. User interface is a little complex, but isn’t difficult to figure out at all. Does require accounts for reporting, but accounts are linked to Lodestone profiles, making it easier to tell if the site is being trolled or not. Of note: as of May 2019, the site is prone to long load times and frequent downtime, usually due to the (probably unexpected) volume of user traffic.
FFXIV Hunts Pathfinder - For daily hunts, shows you the simplest ways to get them all knocked out in a manner that doesn’t make you want to punch Yoshi-P. Has ARR, HW, and SB pathfinders.
Cable Monkey’s Hunt Maps - Never ask where Squonk is again! Spawn points for ARR, HW, and SB hunt marks, B, A, and S ranks. THIS SITE WILL NOT BE UPDATED FOR SHADOWBRINGERS
FFXIV Hunts - Almost identical to Cable Monkey’s site, but a much more user-friendly layout, with collapsible sections by expansion.
Sightseeing Log Helper - Where to go, when to go, what emote to use. Also keeps track of which sightseeing log entries you’ve done, and can filter them out.
Eureka Tracker - THE Eureka tracker website. Create and share NM spawns in each zone, check the weather, even tell people if the local Pazuzu is up or not! Also has a logos tracker!
FFLogos - For keeping track of what mnemes you’ve got, what you need, and what actions you’ve unlocked. Will tell you if you can make something based on your input of what you’ve got in your inventory.
Eorzea Music - Excellent way to keep track of what orchestrion rolls you have and don’t have, as well as where to get all of them. Asks you to create an account, but is free.
Apkallu Falls - A rather comprehensive collection of collection trackers. Does require a login for manual tracking, but covers just about everything you would want to collect except Triple Triad cards.
XIV Style - A comprehensive catalogue of What The Heck Does It Look Like, very neatly sorted and categorized.
Eorzea Collection - We all know glamour is the true endgame, and this is the catalogue to look at if you want glamour inspiration or just want to see what other people are wearing. Basically the Vogue Magazine for FFXIV.
Miraprisnap - Very similar to Eorzea Collection; a gallery for inspiration, but entirely in Japanese, with no translation available.
FFXIV Squadron - A website that does annoying squadron math for you! Find out if you actually can do that mission or not the (relatively) easy way.
Chocobo Color Calculator - Accurate results for what to stuff your birb with to get the color you want, plus or minus RNG. Because it’s not really FFXIV if there isn’t RNG in it.
FF14 Housing - Images of housing items in the game, as well as where to get them. Updated regularly, very comprehensive.
Housing Snap - A housing magazine, basically, chock full of ideas, inspirations, and really pretty pictures. Of note: the website is in Japanese, and does not seem to have any translations to select from.
Skywatcher Plus - Just in case you want something that does nothing but tell you the weather. Does not include Eureka weather.
Character Card Generator - Fun little character card generator.
Instant Sloppy - Because this list would absolutely not be complete without this. You already know what it does.
Special thank-yous for contributing go to:
@roses-and-grimoires - recommended Apkallu Falls
@ooc-llorne - recommended Housing Snap and Teamcraft
@renofmanyalts - clarification of % rates noted on FFXIV Gardening
@egg-soda - for suggesting Miraprisnap