Useful Drupal modules

Click on the module name for notes, comments, patches.
Recommendations (for and against) are my personal opinion only and may be out of date. Feel free to email with corrections/suggestions.

Why haven't you mentioned Drupal 9? As of February 2022 I've updated all the sites I look after to Drupal 9 (experience: mixed). I haven't decided how to label future version compatibility as D10 will be coming soon as well. The upgrade_status module is superb. You're bound to have issues with composer. Also watch out for a nasty session headers bug with redirect_after_login.

What about sites still running Drupal 7? In short I still recommend leaving them on Drupal 7. Your decision is really if you will gain anything from Drupal 8/9 and for many then answer will be no, and one of the main hassles - apart from converting each content type one at a time, and setting up a new theme, will be recreating all your views by hand, as views can't be automatically upgraded.

(1 modules in list)
Module name or machine name
Any text in the notes
Name D8 Personally Tested Last Updated
Password policy (password_policy) 2018-11-26

d.o. page

Not recommended

There are still quite a few bugs open. I dropped this for a project, partly because it adds a load of clutter with the 'resets' and reset dates.
The minimum password policy in Drupal is already 12 characters anyway (and one issue is changing the minimum length doesn't change the help text.) 
You need to enable the submodules to use the various constraints:
drush pm:list | grep 'password_policy_'
Admin users see password policy stuff on the user profile page.
You need to set password reset days to 0 if you don't want to enforce a reset policy.
Policies can be applied by role.  
You get a generic warning about the password 'not matching the password policy'. Suggest using string overrides to change the "To change the current user password, enter the new password in both fields." message users see.
Instructions: add/edit the policy, click next, choose constraint then click 'Configure constraint settings' otherwise you won't be able to change anything.
It also lets you do a forced reset by role.