SponsorBlock. An absolute necessity if you watch youtube on desktop. It skips host-read sponsors in videos, as well as other stuff you might want to skip like intro animations and Interaction Reminders ("don't forget to like and subscribe!").
Stylus: Redesign your favorite websites with Stylus, an actively developed and community driven userstyles manager.
Tampermonkey: Tampermonkey is the world's most popular userscript manager.
Advanced
Request Control: An extension for controlling requests. See also Redirector, not as powerful, but much more user friendly.
Modify Header Value (HTTP Headers): Add, modify or remove a header for any request on desired domains. I use this one to force sites to load only the image when opening images in new tabs.
Cookie AutoDelete: Control your cookies! This WebExtension is inspired by Self Destructing Cookies. When a tab closes, any cookies not being used are automatically deleted. Keep the ones you trust (forever/until restart) while deleting the rest. Containers Supported
uBlock Origin: Finally, an efficient wide-spectrum content blocker. Easy on CPU and memory.
uMatrix: [EDIT-WARNING: as pointed by @sovietknuckles@hexbear.net, uMatrix it's not longer maintainedsince 2021] Point & click to forbid/allow any class of requests made by your browser. Use it to block scripts, iframes, ads, facebook, etc.
Besides the one super-obvious (uBlockOrigin), my favorite single one would be Tab Center Reborn, which together with the styling from Firefox Vertical Tabs pretty accurate recreates the superb vertical tabs of MS Edge.
And on a desktop screen, I can't imagine going back to horizontal tabs that waste the previous vertical space I got.
ublock obviously should be installed on Firefox by default. But I seem to have a host of privacy add-ons that break few-to-no websites.
Privacy Possum , which blocks certain tracking headers/js. Privacy Badger by the EFF is an acceptable alternative but I've personally found it doesn't block quite as much.
NoScript Honestly my favourite addon of all time. You can operate in block-everything mode and just allow javascript/HTML5 from sites you trust, or if you're lazy then just operate in allow-everything mode and every now and then set crummy sites to untrusted (looking at you google tag manager). In block-everything-by-default mode, this add-on will break some sites, but the UI is so easy it's a couple of clicks to trust all the sites in a tab and auto-refresh.
Be warned - If you're not privacy conscious, you might cry from seeing the hundreds of sites that are running javascript on your machine without asking.
User-Agent Switcher Really easy add-on to just leave on and misdirect sites. Never caused me a single problem, and in fact is useful when sites (looking at you Microsoft Teams) claim they don't work in Firefox and refuse to load but actually work fine if you use this addon and pretend to be Chrome.
Sponsorblock kicks ass. 30 hours of ads skipped in half a year.
I have a few others installed that have already been mentioned plenty of times like SponsorBlock, uBlockOrigin. Not using an ad filter these days is like fucking a stranger without a condom, you're just asking for super syphilis.
uBlock Origin: On medium mode. Honestly, the internet mostly sucks without this excellent extension.
Dark Reader: Easy on your eyes and prolongs battery life on OLED displays.
Redirector: This allows you to be in full control of which sites/urls you redirect and to where. As it allows the use of regex, you're even able to create your own 'bangs'. For example I used !x as a bang to redirect me to my favorite SearXNG instance. Kinda neat.
Blocktube. Simple and advanced blocking of videos on youtube. Worth getting. Also stops youtube from auto pasuing after having watched a while.
Consent-o-matic. Set your preferences and it will automatically click those specific preferences when you visit a website, where it recognizes the cookie accept popup. No more need to click accept all, to move on. (It does not know all types of cookie pop ups, but it knoes the ones used by a large chunk of websites)
Imagus. Mouse over an image and this extension will attempt to show it (on your mouse location) in larger size. This works great for various things. News articles, social media etc. It can even do it for video and gifs. It can be annoying in some cases but.. ive gotten used to it. I used to use it on reddit. Just mouse over the posts titles and the pic would pop up. And as said before, super nice for articles and photo albums etc
Sideberry, its like Tree Style Tabs but IMO is much more configurable and refined. It's honestly changed the way I use browsers, being able to bookmark entire trees of tabs, toggle between tab sets, and manually load/unload trees and groups. I legitimately worry about the extension api changing and disallowing it.
Cannot say whether someone has already said it or not, but Flagfox. I like to know if possible whether or not a site is hosted in certain countries or just might be curious sometimes as to where the site server is located.
Open in Reader View, which allows me to open a link directly in reader view. This can actually bypass some login walls surprisingly enough.
Activate Reader View, which allows me to force a website to render in reader view even if the browser decides not to show the icon in the address bar.
LocalCDN which hosts some CDN resources locally (it's a more frequently updated fork of Decentraleyes)
Open With, which allows me to open a url in another browser or another command. I mainly use it for feeding urls to yt-dlp.
Web Archives, which allows me to open a link in Archive.org among other archive services.
LibRedirect, which allows me to open links in privacy frontends (up-to-date fork of Privacy Redirect)
For mobile only,
OldLander, which makes old.reddit.com more usable in mobile. I started having issues with almost every teddit instance once the API changes came in, so I decided to bypass the frontends and use reddit directly.
I've been using IPvFoo on all my PCs since I wrote it for Chrome 12 years ago. Recently I made it fully Firefox compatible. It's useful if you have IPv6 and want to see which websites are on board, though it's a bit depressing if your ISP only offers IPv4.
I've found it particularly interesting on Lemmy, because it connects to such a wide variety of independent servers:
I don't think I've seen this mentioned, likely because it's a simple, non-privacy extension.
Reading List. It works like bookmarks, but it is targeted at news articles and other things you want to read but don't necessarily want to "forever save".
Chameleon, great privacy tool, but can break some crappy sites, unless you can configure it so it doesn't.
ScrollAnywhere, a mobile like scrolling with middle mouse button. I find it more efficient and intuitive.
Ublock ofc
(Forgot name), an addon that lets you skip link shorteners with ads.
Literally all I have ever used. I love mouse gestures so much because of Opera. I was using that for a bit before I discovered Firefox back in the day.
Others have already mentioned some excellent vertical tab add-ons, so I'll post Tabs Aside, which is a super convenient way to save and load a window full of tabs. Saves having like 20 windows open with different stuff you don't want to lose.
Some of these are specialized tools, but to start, I make big, big use of dedicated containers, Google, Amazon, Reddit, Pixiv, Tumblr, and Discord. Sidebar note, uBlock Origin, NoScript, Bypass Paywalls Clean, Container Sidebar, Downloads Sidebar, Get RSS Feed URL, Pixiv Toolkit, FediShare, Tumblr - Post to Tumblr, Twitter Gif & Video Downloader, and Video Downloadhelper