Magic Login is a service that allows you to send transactional e-mails with templates and support for authentication tokens built-in.
What that means is that you can send e-mails that contain a button (that is a link to a URL), and based on the token in this URL you can verify that it was in fact this e-mail's owner that clicked the link.
That's exactly what you need for:
User sign up (and associated e-mail verification)
E-mail confirmation for actions (e.g. deleting their account, or making other dangerous changes)
Password reset e-mails
E-mail sharing or account invites (e.g. click link in e-mail to get access to this document).
To make use of Magic Login you will need an account. There is a free trialthat doesn't require payment details, use that to try it out.