Which folders on a Mac need backing up

Short answer: your home folder, which is /Users/yourname, covers nearly everything that is actually yours.

The interesting part is the handful of things inside it that people exclude by accident, and the couple of large things there is no point copying at all.

The four everybody thinks of

These are what people mean when they say "my files", and any backup tool defaults to them:

~/Documents
~/Desktop
~/Pictures
~/Downloads

~ is your home folder. ~/Downloads is arguable: for most people it is a junk drawer, and for some it is where every important attachment they have ever received actually lives. Look in yours before deciding.

The ones people forget

This is the useful half of the page. Each of these is inside your home folder, so a backup of the whole home folder gets them, and a backup of "just Documents and Desktop" does not.

Mail, if you use Apple Mail. ~/Library/Mail. On an IMAP account the server has a copy, so this matters most for local mailboxes, On My Mac folders, and years of archived post nobody is holding but you.
Messages. ~/Library/Messages. Where the entire iMessage history lives when it is not in iCloud.
Your Photos library. ~/Pictures/Photos Library.photoslibrary. It is a package, and it copies as one item. Important: if Optimize Mac Storage is on, the full-resolution originals are not on the Mac and copying this gets you previews. Turn it off and let the Mac download everything before you rely on a copy of it.
Browser profiles. ~/Library/Application Support/Google/Chrome, ~/Library/Application Support/Firefox, ~/Library/Safari. Bookmarks, history, and extension settings.
Developer keys and configuration. ~/.ssh, ~/.gnupg, ~/.config, ~/.zshrc. Small, invisible in Finder, and painful to reconstruct. Finder hides them; press Cmd Shift Full Stop to see them.
App support data. ~/Library/Application Support generally. This is where a lot of apps keep the thing you actually made, as opposed to the app itself.

The pattern is that ~/Library is hidden, is not what anybody pictures when they think of their files, and contains a great deal of the work.

What is not worth copying

Applications. Re-download them. They are large, they are replaceable, and an App Store app restored as files often will not run correctly anyway.
Caches. ~/Library/Caches. Regenerated on demand, frequently enormous, and pure noise in a backup.
Virtual machine images and game libraries. Hundreds of gigabytes that are either replaceable downloads or better handled deliberately. Excluding these is usually the single biggest win when a backup will not fit.
The system itself. /System and /Library. macOS always comes back from Apple, and no backup tool can put a sealed system volume back.
Anything already syncing, if it is your only copy of it. Sync is not a backup. A Dropbox folder is on your disk, so back it up like anything else, and do not count it as a second copy.

The short answer, in one line

Back up your whole home folder, and exclude caches, virtual machine images and anything you can re-download. That is one decision, and it is right for nearly everybody:

rsync -aE --exclude 'Library/Caches' ~/ /Volumes/Backup/home/

Note the missing --delete. On an archive you very rarely want a mirror, because a mirror carries out your deletions for you the next time it runs.

The part the list does not solve

Choosing folders is the easy half. The hard half is that whatever you chose is now a decision made once, months ago, that quietly decides what you get back. New Mac, new project directory outside the home folder, an app that moved its data: none of that updates the list.

Copy Shelter shows what is protected on its main screen, alongside where the copies are, alongside where the copies are and when each was last verified. It warns when a destination sits on the same disk as the folder you are protecting, and it says so when a location has not been seen for a week. The list being visible is most of what stops it going stale.

Common questions

Should I back up my whole hard drive?

You cannot back up all of it in a useful sense, because Apple seals the macOS system volume. What you can and should copy is everything under your home folder. Adding the system adds size and gets you nothing you could restore.

Do I need to back up my Applications folder?

Generally no. Re-download them, which is faster than restoring them and avoids the licensing and signature problems that come with copying apps between machines. Back up their data instead, which lives in ~/Library/Application Support.

What about files in iCloud Drive or Dropbox?

Back them up. Sync is not a backup: a deletion or a corruption propagates to every device within seconds, and version history on these services is a window of about 30 days. If a file only exists in a sync folder, it exists once.

How do I see hidden folders in Finder?

Press Cmd Shift Full Stop in any Finder window. It toggles hidden items, which is how you see ~/.ssh and the rest. Press it again to hide them.

How much space will I need?

Roughly what your files take, if the tool sizes by data. Check with du -sh ~ in Terminal. Time Machine is the exception: it sizes by the whole disk being copied, ignoring how full it is, which is why it refuses drives that look big enough.

Which folders on a Mac actually need backing up