I was always annoyed by the registration form. Especially when you need to get some features of a registered user, but only for one time, for example, download some software or ask a question on a highly specialized forum. In most cases, registration forms there are simply terrible, although they are not very diverse. Having no desire to fill out five or six fields marked with an asterisk, I am forced to grit my teeth two (!) Times to enter an email address, solve a captcha and come up with a secret question. And after all these torments, after clicking on the cherished “submit” button, the page reloads completely and happily reports that the captcha is entered incorrectly, and the username has long been taken. And on top of the torment they demand from me to follow the link sent to my mail to activate my account.
I have a
small online store selling items not at all everyday use. That is, just one where registration is necessarily needed, but most likely, the user will use it once. In this case, the registration form takes the form:

The checkbox "I am not a robot" performs the function of a captcha, but its relevance can be argued. After clicking on the button, javascript checks the correctness of entering the mail address and the state of the check box; in case of success, the data is sent by Ajax to the server, where it is checked again. If the mailing address is entered correctly and has not yet been registered, a new account is created, a password is generated, which is sent to the user's mail, and the new user is authorized. In this way, both parties win - the visitor is free from the torment of registration, and the site gets a more loyal user.
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But the online store is not enough to know only the email address of the buyer. For the delivery of goods, you also need the client’s address, telephone number and, finally, the name. These data are obtained directly at the time of order:

And of course, the user can change his password in the profile, specifying the password generated during registration (for which he will need to check email, actually confirm it), and the delivery information will not have to be specified a second time.
UPD: Thanks for the comments. Checkbox is no more)
UPD2: Logical continuation:
about captcha