Nowadays almost all email services require your phone number to verify identity & then only you can sign up. It is the case with Gmail or Yahoo Mail. Most of the time we are fine with sharing our phone number with email service providers. But sometimes, we may have a case where we want to get a free email address on a temporary basis or for some additional requirement. We might want to get an email where we don’t need to share our phone number for privacy reasons.
There are some email services out there without mandatory phone verification. I just wanted to mention one of them which I used personally & liked their service. It is called Tutanota. What I mostly liked about them is that they take security as a priority & your inbox is stored encrypted in their server except mail addresses. You can read more about it here https://tutanota.com/security. And another thing is that they don’t show any advertisement which is a pretty good thing.
For free accounts you can get a mailbox with 1 GB space. That should be good enough if you are looking for something additional on top of your primary email address.