Microsoft's email servers do not reliably deliver email. There are numerous reports on the web of email being successfully delivered to Microsoft's servers, but failing to show up in a user's inbox - even in the spam folder.
You may be able to work around this by clicking on the cog icon in your inbox, going to "Safe and blocked senders", and adding
email@example.com to the list of safe senders. You can then visit AnkiWeb's verification page and refresh it until another verification email is sent.
If problems persist, you will need to use a different email provider (such as a free gmail.com account) that reliably delivers email.
Verifying your email may be frustrating, but it is important to have a working contact method - without one, you would not be able to recover your account if you forgot your password.