Generally Useful

ContextSearch web-ext

Select text and search from the context menu or a tiled popup using any of your installed search engines.

Drag-Select Link Text

Easily select the text in links. So damn useful when you need to copy and paste some text that is part of a link!

Gesturefy

Mouse gestures to control the browser. Less moving hands between mouse and keyboard.

New Tab Override

New Tab Override brings back the ability to change the page which is shown when opening a new tab.

Textarea Cache

Automatically save the content in a text input field. Saves you having to retype it when a web-site barfs and the text would be otherwise lost.

Remove annoyances

I don't care about cookies

Get rid of annoying cookie warnings from almost all 'infected' websites!

Make Medium Readable Again

Improves the Medium reading experience, ruined by user engagement tactics.

Neat URL

Neat URL cleans URLs, removing parameters such as Google Analytics' utm parameters.

Unstick!

Click the toolbar button, and any element with 'position: fixed' is removed from the page. Clears up pages cluttered with frozen headers and share buttons. (For some reason, I usually have to click it twice for it to have an effect.)

A bit more specialist, but useful to some

Bookmark Tab Here

Adds context menu item 'Bookmark Tab Here' to Bookmarks Menus as an alternative bookmarking method.

Easy Youtube Video Downloader Express

Seems to be the best of the add-ons to download video from youtube.

Feed Preview

Because RSS feeds are not dead.

Firefox Multi-Account Containers

If you have multiple accounts on the same site, then this can really save you having to log out and log in again to switch accounts all the time.

Markdown Here

If you are a markdown aficionado this lets use write in markdown then click a button to toggle to formatted. Useful for web-based email (gmail, etc) and other sites like blogger or wordpress.

SiteDelta Watch

Regularly monitors a page for changes.

More developer specific

Empty Cache Button

Toolbar button to empty the browser cache.

Html Validator

HTML validation inside Firefox. The number of errors of a HTML page is seen on the form of an icon and details in a developer tools tab.

Open With

Quickly open current web page in another browser.

Security/Privacy

uBlock Origin

Repeat after me, it is not an 'ad blocker', it is a HTML firewall.

Bitwarden Passward Manager

The best password manager IMO.

Cookie AutoDelete

When a tab closes, any cookies not being used are automatically deleted. Whitelist the ones you trust while deleting the rest. (Note: It can generate strange behaviour on some sites, or pop-ups that normally only show once will repeat.)

Decentraleyes

Protects you against tracking through "free", centralized, content
delivery. It prevents a lot of requests from reaching networks like
Google Hosted Libraries, and serves local files to keep sites from
breaking.

HTTPS Everywhere

Enables HTTPS encryption automatically on sites that are known to
support it, even when you type URLs or follow links that omit the https:
prefix.

Privacy Badger

Automatically learns to block invisible trackers.

Others I haven't used by are on my list to try

HTTPS by default

Request websites over secure https by default from the location bar instead of insecure http.

Facebook Container

Prevent Facebook from tracking you around the web. The Facebook
Container extension for Firefox helps you take control and isolate your
web activity from Facebook.